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# Transformations and Angle Relationships

## Objective

Define and use the exterior angle theorem for triangles.

## Common Core Standards

### Core Standards

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• 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.

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• 7.G.A.2

• 7.G.B.5

## Criteria for Success

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1. Extend line segments of a polygon to see exterior angles.
2. Know that exterior angles are supplementary to the adjacent interior angle.
3. Know that exterior angles of a triangle are equal to the sum of the two opposite interior angles.
4. Use the exterior angle sum theorem and other properties of angles to determine additional angle relationships.

## Tips for Teachers

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#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Triangle ${ABC}$ has two interior angles that measure ${14^{\circ}}$ and ${30^{\circ}}$.

1. What is the measure of the exterior angle marked by $x$?
2. What is the relationship between the value of $x$ and the two given interior angles?

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic C > Lesson 14Teacher Version: Example 1

Grade 8 Mathematics > Module 2 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

### Problem 2

Triangle ${ABC}$ has an interior angle that measures ${45^{\circ}}$ and an exterior angle that measures ${129^{\circ}}$
What is the measure of the interior angle marked by $x$?

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 2 > Topic C > Lesson 14Teacher Version: Example 4

Grade 8 Mathematics > Module 2 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Triangle ${ABC}$ is shown in the diagram below. Show two different ways that you can determine the measure of $\angle {ABC}$.