### Identifying Alternate Exterior Angles#### IntroductionIn this exercise, we will identify the alternate exterior angle to a given angle. This concept is vital in understanding the properties of parallel lines intersected by a transversal.#### Diagram and Problem StatementRefer to the diagram provided. There are two parallel lines, indicated as `N` and `M`, intersected by a transversal line `L`. The angles are labeled as follows:- Above line `N` on the left side of the transversal: angle 1- Above line `N` on the right side of the transversal: angle 2- Below line `N` on the left side of the transversal: angle 3- Below line `N` on the right side of the transversal: angle 4- Above line `M` on the left side of the transversal: angle 5- Above line `M` on the right side of the transversal: angle 6- Below line `M` on the left side of the transversal: angle 7- Below line `M` on the right side of the transversal: angle 8The task is to find the alternate exterior angle to angle 8.#### SolutionAlternate exterior angles are pairs of angles that:- Lie on opposite sides of the transversal- Are outside the parallel lines and not adjacentIn the context of this problem, for angle 8, the alternate exterior angle lies on the opposite side of the transversal and outside the parallel lines.From the diagram:- Angle 8 is on the right side of the transversal, below the line `M`.- Therefore, its alternate exterior angle must be on the left side of the transversal, above the line `N`.Hence, the alternate exterior angle to angle 8 is angle 1.#### ChoicesA. angle 1 (Correct answer)B. angle 2C. angle 4D. angle 7#### ConclusionUnderstanding alternate exterior angles helps in comprehending the properties of parallel lines and transversal intersections. In this scenario, angle 1 is the correct alternate exterior angle to angle 8.

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Name the alternate exterior angle with angle 8. 4 3 5/6 7/8

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Identifying Alternate Exterior Angles

#### Introduction

In this exercise, we will identify the alternate exterior angle to a given angle. This concept is vital in understanding the properties of parallel lines intersected by a transversal.

#### Diagram and Problem Statement

Refer to the diagram provided. There are two parallel lines, indicated as `N` and `M`, intersected by a transversal line `L`.

The angles are labeled as follows:
- Above line `N` on the left side of the transversal: angle 1
- Above line `N` on the right side of the transversal: angle 2
- Below line `N` on the left side of the transversal: angle 3
- Below line `N` on the right side of the transversal: angle 4
- Above line `M` on the left side of the transversal: angle 5
- Above line `M` on the right side of the transversal: angle 6
- Below line `M` on the left side of the transversal: angle 7
- Below line `M` on the right side of the transversal: angle 8

The task is to find the alternate exterior angle to angle 8.

#### Solution

Alternate exterior angles are pairs of angles that:
- Lie on opposite sides of the transversal
- Are outside the parallel lines and not adjacent

In the context of this problem, for angle 8, the alternate exterior angle lies on the opposite side of the transversal and outside the parallel lines.

From the diagram:
- Angle 8 is on the right side of the transversal, below the line `M`.
- Therefore, its alternate exterior angle must be on the left side of the transversal, above the line `N`.

Hence, the alternate exterior angle to angle 8 is angle 1.

#### Choices

A. angle 1 (Correct answer)
B. angle 2
C. angle 4
D. angle 7

#### Conclusion

Understanding alternate exterior angles helps in comprehending the properties of parallel lines and transversal intersections. In this scenario, angle 1 is the correct alternate exterior angle to angle 8.

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