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
Related questions
Question
![### Problem 8
**Objective:**
Find the measure of angle \( \angle C \).
**Diagram Explanation:**
The diagram shows a triangle \( \triangle ABC \) with the following angle expressions:
- Angle \( \angle BAC \) is labeled as \( (9x - 26)^\circ \).
- Angle \( \angle ABC \) is labeled as \( (2x - 12)^\circ \).
- Angle \( \angle ACB \) is labeled as \( (4x + 43)^\circ \).
**Solution:**
Given that the sum of angles in a triangle is always \( 180^\circ \), we can write the equation:
\[
(9x - 26) + (2x - 12) + (4x + 43) = 180
\]
By simplifying and solving for \( x \), the value of \( x \) is used to find the measure of \( \angle C = (4x + 43)^\circ \).
**Answer:**
\( m \angle C = 13^\circ \)
---
**Note:**
The problem is part of an educational resource by Gina Wilson, All Things Algebra®, from 2014-2020.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ad698c-f3a1-4d43-b8a5-74ae405449f9%2F46638c0f-e7eb-4c22-a6ad-00f295357ecc%2Fc5pfb4_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 8
**Objective:**
Find the measure of angle \( \angle C \).
**Diagram Explanation:**
The diagram shows a triangle \( \triangle ABC \) with the following angle expressions:
- Angle \( \angle BAC \) is labeled as \( (9x - 26)^\circ \).
- Angle \( \angle ABC \) is labeled as \( (2x - 12)^\circ \).
- Angle \( \angle ACB \) is labeled as \( (4x + 43)^\circ \).
**Solution:**
Given that the sum of angles in a triangle is always \( 180^\circ \), we can write the equation:
\[
(9x - 26) + (2x - 12) + (4x + 43) = 180
\]
By simplifying and solving for \( x \), the value of \( x \) is used to find the measure of \( \angle C = (4x + 43)^\circ \).
**Answer:**
\( m \angle C = 13^\circ \)
---
**Note:**
The problem is part of an educational resource by Gina Wilson, All Things Algebra®, from 2014-2020.
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