angle relationships homework

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Pairs of Angles Worksheets

Plenty of practice awaits your 7th grade and 8th grade students in these printable pairs of angles worksheets that bring together every exercise you need to assist them in getting their head around the different types of angle pairs and the properties associated with each. This resource comes particularly handy to practice identifying angle pair relationships, gain knowledge of their properties, and find the measure of unknown angles. Access some of these worksheets for free!

» Vertical Angles

» Adjacent Angles

» Linear Pairs of Angles

» Complementary & Supplementary Angles

Identifying Pairs of Angles

Can your students tell an adjacent angle from a vertical angle or a linear pair? Remodel your recapitulation process with this bundle of printable pairs of angles worksheets! They need to analyze and state the relationship between the indicated angles.

• Download the set

Finding the Measure of Indicated Angles in a Pair

Applying the properties of pairs of angles, and equating the unknown angles with angles whose measures are known is what students are expected to do in this section of pdfs to find the indicated angle.

Pairs of Angles and Linear Expressions

How about adding a dash of algebra to geometry? Try these printable worksheets on pairs of angles involving linear expressions and practice applying the angle addition postulate, and appropriate properties to solve for x.

Add-On Practice Worksheets

» Complementary and Supplementary Angles

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Calcworkshop

Angle Relationships Simply Explained w/ 11+ Step-by-Step Examples!

// Last Updated: January 21, 2020 - Watch Video //

In today’s lesson, you’re going to learn all about angle relationships and their measures.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

We’ll walk through 11 step-by-step examples to ensure mastery.

Let’s dive in!

Angle Pair Relationship Names

In Geometry , there are five fundamental angle pair relationships:

• Complementary Angles
• Supplementary Angles
• Adjacent Angles
• Linear Pair
• Vertical Angles

1. Complementary Angles

Complementary angles are two positive angles whose sum is 90 degrees.

For example, complementary angles can be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two acute angles, like ∠MNP and ∠EFG, whose sum is equal to 90 degrees. Both of these graphics represent pairs of complementary angles.

Complementary Angles Example

2. Supplementary Angles

Supplementary angles are two positive angles whose sum is 180 degrees.

For example, supplementary angles may be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two angles, like ∠MNP and ∠KLR, whose sum is equal to 180 degrees. Both of these graphics represent pairs of supplementary angles.

Supplementary Angles Example

What is important to note is that both complementary and supplementary angles don’t always have to be adjacent angles.

3. Adjacent Angles

Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points.

Angles 1 and 2 are adjacent angles because they share a common side.

Adjacent Angles Examples

And as Math is Fun so nicely points out, a straightforward way to remember Complementary and Supplementary measures is to think:

C is for Corner of a Right Angle (90 degrees) S is for Straight Angle (180 degrees)

Now it’s time to talk about my two favorite angle-pair relationships: Linear Pair and Vertical Angles.

4. Linear Pair

A linear pair is precisely what its name indicates. It is a pair of angles sitting on a line! In fact, a linear pair forms supplementary angles.

Because, we know that the measure of a straight angle is 180 degrees, so a linear pair of angles must also add up to 180 degrees.

∠ABD and ∠CBD form a linear pair and are also supplementary angles, where ∠1 + ∠2 = 180 degrees.

Linear Pair Example

5. Vertical Angles

Vertical angles are two nonadjacent angles formed by two intersecting lines or opposite rays.

Think of the letter X. These two intersecting lines form two sets of vertical angles (opposite angles). And more importantly, these vertical angles are congruent.

In the accompanying graphic, we see two intersecting lines, where ∠1 and ∠3 are vertical angles and are congruent. And ∠2 and ∠4 are vertical angles and are also congruent.

Vertical Angles Examples

Together we are going to use our knowledge of Angle Addition, Adjacent Angles, Complementary and Supplementary Angles, as well as Linear Pair and Vertical Angles to find the values of unknown measures.

Angle Relationships – Lesson & Examples (Video)

• Introduction to Angle Pair Relationships
• 00:00:15 – Overview of Complementary, Supplementary, Adjacent, and Vertical Angles and Linear Pair
• Exclusive Content for Member’s Only
• 00:06:29 – Use the diagram to solve for the unknown angle measures (Examples #1-8)
• 00:19:05 – Find the measure of each variable involving Linear Pair and Vertical Angles (Examples #9-12)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Angle Relationships Handout

Use this one-page geometry handout to help students determine angle relationships with confidence and ease! This helpful resource describes and illustrates four different angle relationships: complementary angles, supplementary angles, vertical angles, and adjacent angles. Students will learn the properties of the four angle relationships and review visual examples of each. This handout makes a great study guide or reference sheet that students can use in their geometry unit on angles. For a guided notes version of this handout in which learners can record their own definitions, check out Angle Relationships Guided Notes !

View aligned standards

Easy Peasy All-in-One Homeschool

A complete, free online christian homeschool curriculum for your family and mine, angle relationships.

In this lesson, you will extend your knowledge of different types of angles to learning about relationships among pairs of angles. You will also learn to write and solve equations that will allow you to find the measure of unknown angles in different figures composed of angles.

We will start out with a quick review of basic angles. Remember that angles are formed by two rays with a common endpoint (vertex).  Congruent angles  are angles that have the same measure. It is important to remember that when naming angles, the vertex always goes in the middle. If you need a bit more review for angle classifications, please watch the following video. Once you have seen how to name and classify angles, we will move forward to angle pairs.

In earlier years, you learned how to recognize right angles, obtuse angles, acute angles, and straight angles. We know that a right angle measures 90° and a straight angle always measures 180°.

An acute angle is an angle that measures less than 90°. How can you use the idea of a right angle to help you identify an acute angle? If the opening of an angle is smaller than the opening of a right angle, it is acute.

The same goes for an obtuse angle. This is an angle that measures more than 90 but less than 180. If the opening of an angle is larger than the opening of a right angle, but smaller than the opening of a straight angle, the angle is obtuse.

Let us look at some of the relationships that are common among angles .

Adjacent angles  are pairs of angles that share a vertex and one side but do not overlap. In the examples below, angles a and b are adjacent angles.

Complementary angles are two angles whose measures have a sum of 90°. The image below shows two complementary angles. They are both acute (each measuring less than 90°) and when you add them together, they equal 90°.

Supplementary angles , (also known as linear pairs ), are two angles whose measures have a sum of 180°. Remember, the key word is “pair”, which means two angles. Like complementary angles, these angle pairs do not have to be adjacent. In the image below, angle a and angle b have a sum of 180°.

Here are some basic word problems that we can solve without diagrams.

Angles  A  and  B  are supplementary. If m ∠  A  is 32 °, what is the m ∠  B  ?

Given the fact that they are supplementary, we know that the two add up to 180°. You can set up an equation to read:

B + 32 = 180 and solve for B. -32     -32

B          = 148

Angles C and D are complementary. If m ∠C is 22 °, what is the m ∠ D ?

Given the fact that they are complementary, we know that the two add up to 90°. You can set up an equation to read:

D + 22 = 90 and solve for D -22   -22

D         =  68

You can also use diagrams to find unknown angle measures in complementary and supplementary angles.

Angles LGM and MGH are complementary.

Create an equation to solve for x.

x + 64.9 = 90 -64.9   -64.9

Take a look at the video lesson to see examples of complementary and supplementary angles .

Practice Adjacent, Complementary, and Supplementary Angles

Now, practice what you have learned about adjacent, complementary, and supplementary angles using the following diagram.

1. Name the right angles.

2. Name 5 pairs of adjacent angles.

3. Name a pair of complementary angles.

We have learned about angle pairs. Now, let us go a bit deeper and learn to use line and angle relationships to solve problems with figures. First of all, we know that adjacent angles have a common vertex and a common ray.

Math  /  8th Grade  /  Unit 3: Transformations and Angle Relationships

Transformations and Angle Relationships

Students investigate congruence and similarity by studying transformations of figures in the coordinate plane, and apply these transformations to discover new angle relationships.

Unit Summary

In Unit 3, 8th grade students bridge their understanding of geometry from middle school concepts to high school concepts. Until now, standards in the geometry domain have been either supporting or additional to the major standards. In 8th grade , geometry standards, especially the standards highlighted in this unit, are part of the major work of the grade and play a critical role in setting students up well for success in high school .

In this unit, students begin their work with transformations using patty paper (transparency paper) to experiment with, manipulate, and verify hypotheses around how shapes move under different transformations (MP.5). They use precision in their descriptions of transformations and in their justifications for why two figures may be similar or congruent to each other (MP.6). Students then apply their understanding of transformations to discover new angle relationships in parallel line diagrams and triangles.  

Prior to 8th grade, students developed their understanding of geometric figures and learned how to draw them, calculate measurements, and model real-world situations. In 7th grade , students were introduced to the concept of scaling through scale drawings, and they solved for various measurements using proportional reasoning. Students will draw on these prior skills when they investigate dilations and similar triangles. 

In high school geometry , students spend significant time studying congruence and similarity in-depth. They build off of the informal proofs and reasoning developed in 8th grade to hone their definitions of transformations, prove geometric theorems, and derive trigonometric ratios.

Pacing: 26 instructional days (22 lessons, 3 flex days, 1 assessment day)

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The following assessments accompany Unit 3.

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

• Pre-Unit Assessment
• Pre-Unit Assessment Analysis Guide

Pre-Unit Student Self-Assessment

Have students complete the Mid-Unit Assessment after lesson 10 .

• Mid-Unit Assessment
• Mid-Unit Assessment Answer Key

Use the resources below to assess student understanding of the unit content and action plan for future units.

Post-Unit Assessment

• Post-Unit Assessment Answer Key
• Post-Unit Assessment Analysis Guide

Post-Unit Student Self-Assessment

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Intellectual Prep

Suggestions for how to prepare to teach this unit

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Internalization of Standards via the Post-Unit Assessment

• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit 
• Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

• Read and annotate the Unit Summary.
• Notice the progression of concepts through the unit using the Lesson Map.

Essential Understandings

• Connection to Post-Unit Assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

• Read the UnboundEd Mathematics Guide  Geometry: Unbound A Guide to Grade 8 Mathematics Standards .
• Read the  Progressions for the Common Core State Standards in Mathematics, Geometry, 7-8, High School  for standards relevant to this unit.

The central mathematical concepts that students will come to understand in this unit

• Two figures are congruent to each other if there exists a sequence of rigid transformations that will map one figure onto the other.
• Two figures are similar to each other if there exists a sequence of dilations and rigid transformations that will map one figure onto the other. 
• Certain properties are preserved under rigid transformations (such as angle measurement, line segment length, and parallel line relationships).
• Angle relationships exist in polygons, intersecting lines, and parallel lines that can be used to determine various angle measurements.

Terms and notation that students learn or use in the unit

alternate interior and exterior angles

congruent/ congruence

corresponding angles

rigid transformation

scale factor

translation

vertical angles

To see all the vocabulary for Unit 3 , view our 8th Grade Vocabulary Glossary .

The materials, representations, and tools teachers and students will need for this unit

• Optional : 180° Protractor
• Optional : Calculators (1 per student)
• Graph Paper (2-3 sheets per student)
• Scissors (1 per small group)
• Ruler (1 per student)
• Optional : Tape (1 per small group)
• Optional : Patty paper (transparency paper)

To see all the materials needed for this course, view our 8th Grade Course Material Overview .

Topic A: Congruence and Rigid Transformations

Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).

8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2

Describe and perform translations between congruent figures. Use translations to determine if figures are congruent.

Describe and apply properties of translations. Use coordinate points to represent relationships between translated figures.

8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2 8.G.A.3

Describe and perform reflections between congruent figures. Use reflections to determine if figures are congruent.

Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.

Describe and perform rotations between congruent figures.

Describe sequences of transformations between figures using rotations and other transformations.

Describe a sequence of rigid transformations that will map one figure onto another.

Describe multiple rigid transformations using coordinate points.

8.G.A.2 8.G.A.3

Review rigid transformations and congruence between two figures.

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Topic B: Similarity and Dilations

Define a dilation as a non-rigid transformation, and understand the impact of scale factor.

Describe and perform dilations.

Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.

8.G.A.3 8.G.A.4

Determine and informally prove or disprove if two figures are similar or congruent using transformations.

8.G.A.2 8.G.A.4

Find missing side lengths in similar figures. Find scale factor between similar figures.

Use properties of similar triangles to model and solve real-world problems.

Topic C: Angle Relationships

Define and identify corresponding angles in parallel line diagrams. Review vertical, supplementary, and complementary angle relationships.

8.G.A.2 8.G.A.5

Define and identify alternate interior and alternate exterior angles in parallel line diagrams. Find missing angles in parallel line diagrams.

Solve for missing angle measures in parallel line diagrams using equations.

Define and use the interior angle sum theorem for triangles.

Define and use the exterior angle theorem for triangles.

Define and use the angle-angle criterion for similar triangles.

Common Core Standards

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

8.G.A.1 — Verify experimentally the properties of rotations, reflections, and translations:

8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1.B — Angles are taken to angles of the same measure.

8.G.A.1.C — Parallel lines are taken to parallel lines.

8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.A.3 — Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

Expressions and Equations

8.EE.C.7 — Solve linear equations in one variable.

7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Measurement and Data

4.MD.C.6 — Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Ratios and Proportional Relationships

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Future Standards

Standards in future grades or units that connect to the content in this unit

G.CO.A.2 — Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G.CO.A.3 — Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

G.CO.A.4 — Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.A.5 — Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G.CO.B.6 — Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G.CO.B.7 — Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

G.CO.B.8 — Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

G.CO.C.10 — Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

G.CO.C.9 — Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Similarity, Right Triangles, and Trigonometry

G.SRT.A.1 — Verify experimentally the properties of dilations given by a center and a scale factor:

G.SRT.A.2 — Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G.SRT.A.3 — Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

G.SRT.B.4 — Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

G.SRT.B.5 — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Standards for Mathematical Practice

CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 — Attend to precision.

CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

Solving One-Variable Equations

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Missing Angles in Triangles

Measuring angles, 4th -  5th  , parallel lines, parallel lines & transversals, 9th -  10th  , angle relationships, angles and angle relationships, corresponding angles, properties of angles, triangles, and the..., professional development  .

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• 5. Multiple Choice Edit 45 seconds 1 pt What are complementary angles? Angles that add up to 180° Angles that add up to 90° Angles that are equal to each other Angles that are opposite of each other when lines intersect.
• 7. Multiple Choice Edit 45 seconds 1 pt What are supplementary angles? Angles that add up to 180° Angles that add up to 90° Angles that are equal to each other Angles that are opposite of each other when lines intersect
• 8. Multiple Choice Edit 45 seconds 1 pt What are vertical angles? Angles that are adjacent to each other Angles that add up to 180° Angles that are opposite of each other when lines intersect Angles that add up to 90°
• 9. Multiple Choice Edit 45 seconds 1 pt Is it possible to find the complement angle of 103°? If so, what is it?  Yes, the complement angle is 77° Not possible.  Yes, the compliment angle is 83° Yes, the complement angle is 13°
• 11. Multiple Choice Edit 45 seconds 1 pt What is the supplement angle to 42°? 48° 138° 100° Not possible
• 12. Multiple Choice Edit 45 seconds 1 pt What is the supplement angle to 45°? 45° 180° 135° 100°
• 13. Multiple Choice Edit 45 seconds 1 pt Which phrase is incorrect? Complementary angles have to be adjacent. Supplementary angles equal 180°. Complementary angles can make a right triangle.  Complementary angles add up to be half of 180°.
• 14. Multiple Choice Edit 45 seconds 1 pt What is the complement angle to 12°? 78° 68° 168° 90°
• 15. Multiple Choice Edit 45 seconds 1 pt Do complementary angles have to be adjacent to each other? No Yes
• 16. Multiple Choice Edit 45 seconds 1 pt 2x and 10x are two angles that are supplementary. What do the angles measure? (Hint: 2x + 10x = 180) 30°,150° 5°,10° 15°, 75° 90°, 180°
• 39. Multiple Choice Edit 45 seconds 1 pt What is an "Acute" Angle Angle that measures 180 An Angle that measure 90 An angle that measures more than 90 An angle that measures less than 90
• 40. Multiple Choice Edit 45 seconds 1 pt Angles in the same plane with a common vertex & a common side, but no common interior points. Vertical Complementary Adjacent Suplementary
• 41. Multiple Choice Edit 45 seconds 1 pt In a triangle, how many total degrees are there? 100% 180 degrees it varies 360 degrees
• 42. Multiple Choice Edit 45 seconds 1 pt How many degrees is a straight angle? 90 360 180 145
• 45. Multiple Choice Edit 45 seconds 1 pt Vertical angles are always acute total 180 degrees congruent (equal measures) adjacent angles

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Master angles with interactive Angle Relationships infographics

• Author: Noreen Niazi
• Last Updated at: September 1, 2023

Angle Relationships infographics

Angles are omnipresent, but how do they connect to one another? Do not worry if you have ever become entangled in the web of angle relationships. Angle Relationships Infographics are the ideal technique to make everything completely obvious.

Easily Understanding:

Imagine being able to understand intricate angle ideas using eye-catching infographics. These infographics are a visual treat as well as being educational. They make even the most complicated angle relationships simple for kids, parents, and teachers.

Free and open to all:

What’s best? The resources below for infographics are free! They can be used by students for homework assistance, by parents for fast explanations, and by teachers to incorporate into their courses. Additionally, they are printable, making studying enjoyable and practical.

External Links for Further Exploration:

• Khan Academy – Angle Basics
• Math is Fun – Angle Types

If you have access to the correct tools, understanding angle connections can be a simple. You’ll be a geometry pro in no time with our free printable Angle Relationships Infographics. Check out the suggested external links for even additional clarification. Never before has math learning been so visually appealing!

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Angle Relationships | Worksheets & Homework (Geometry)

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Description

This worksheet & Homework consists of 12 problems that address the following Angle Relationships( Geometry - Unit 1) .

There are 12 problems involving the Angle Relationships + the answer keys .

This worksheet can be used as in-class practice, a quiz, a homework page, or at a math station.

This resource is included in the following bundle(s):

• Click Here for Angle Relationships & Perpendicular and Angle Bisectors | Worksheets & Homework

More Geometry - Unit 1:

• Click Here for Points, Lines, Line segments, Midpoints, Distance, Rays and Planes | Worksheet
• Click Here for Naming and Classifying Angles & Angle Addition Postulate | Worksheets & Homework

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Unit 8 Lesson 2 Homework (Applying Angle Relationships)

Write the equation

Pick 2 answers, write an equation.