**Problem Statement:**Find the value of $ x $.**Diagram Description:**The image displays a triangle with two marked angles. There is an exterior angle formed by extending one side of the triangle:1. One angle of the triangle is marked as $ (8x + 9)^\circ $.2. An exterior angle is marked as $ (5x - 24)^\circ $.3. The other two sides of the triangle are marked with a single line, indicating they are of equal length, forming an isosceles triangle.**Analysis:**In an isosceles triangle, the two base angles are equal. The exterior angle is equal to the sum of the opposite interior angles. Use these properties to find the value of $ x $.

Answered: Image /qna-images/answer/3dd43d05-7a17-454d-87b3-7550cbcb8824.jpg

Answered: (5х - 24)° 8х + 9)°.

Math

Geometry

(5х - 24)° 8х + 9)°.

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

**Problem Statement:**
Find the value of $ x $.

**Diagram Description:**
The image displays a triangle with two marked angles. There is an exterior angle formed by extending one side of the triangle:

1. One angle of the triangle is marked as $ (8x + 9)^\circ $.
2. An exterior angle is marked as $ (5x - 24)^\circ $.
3. The other two sides of the triangle are marked with a single line, indicating they are of equal length, forming an isosceles triangle.

**Analysis:**
In an isosceles triangle, the two base angles are equal. The exterior angle is equal to the sum of the opposite interior angles. Use these properties to find the value of $ x $.

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