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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For #17 I need to solve for x.
![### Geometry Problem: Finding the Indicated Angle
#### Problem 17
You are given two intersecting lines that create vertical angles. The expressions for these angles are as follows:
- One angle measures \( 15x - 5 \) degrees.
- The opposite angle measures \( 13x + 5 \) degrees.
Since these are vertical angles, they are equal.
**Task:** Find the value of \( x \) and the measure of each angle.
#### Solution Steps
1. Set the expressions equal to each other because vertical angles are equal:
\[
15x - 5 = 13x + 5
\]
2. Solve the equation for \( x \).
3. Substitute the value of \( x \) back into either expression to find the measure of the angle.
The task is to compute these values and understand the properties of vertical angles in geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b27e901-e87b-4228-8406-e843591659e6%2F70de2e53-bc2b-404a-8d44-874a0e776614%2Fj757xyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Finding the Indicated Angle
#### Problem 17
You are given two intersecting lines that create vertical angles. The expressions for these angles are as follows:
- One angle measures \( 15x - 5 \) degrees.
- The opposite angle measures \( 13x + 5 \) degrees.
Since these are vertical angles, they are equal.
**Task:** Find the value of \( x \) and the measure of each angle.
#### Solution Steps
1. Set the expressions equal to each other because vertical angles are equal:
\[
15x - 5 = 13x + 5
\]
2. Solve the equation for \( x \).
3. Substitute the value of \( x \) back into either expression to find the measure of the angle.
The task is to compute these values and understand the properties of vertical angles in geometry.
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