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
Find the measure of the marked
![**Problem:**
Find the measure of the marked angles.
**Diagram Explanation:**
The diagram shows two intersecting lines forming vertical angles. The two marked angles in the diagram are labeled as:
- \( (2x + 46)^\circ \)
- \( (7x + 6)^\circ \)
These angles are vertical angles, meaning they are equal.
**Solution:**
1. Set the equations for the vertical angles equal:
\[
2x + 46 = 7x + 6
\]
2. Solve the equation for \( x \):
\[
2x + 46 = 7x + 6
\]
\[
46 - 6 = 7x - 2x
\]
\[
40 = 5x
\]
\[
x = 8
\]
3. Substitute \( x = 8 \) back into either angle expression to find the angle measure:
\[
(2x + 46)^\circ = (2(8) + 46)^\circ = (16 + 46)^\circ = 62^\circ
\]
**Answer:**
The measure of the angles is 62 degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F977ac1a7-2a1a-49aa-9358-74127afd8bcd%2Fffb4f903-4ad6-4b49-b62b-3f5310aff4a9%2F9sua7a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the measure of the marked angles.
**Diagram Explanation:**
The diagram shows two intersecting lines forming vertical angles. The two marked angles in the diagram are labeled as:
- \( (2x + 46)^\circ \)
- \( (7x + 6)^\circ \)
These angles are vertical angles, meaning they are equal.
**Solution:**
1. Set the equations for the vertical angles equal:
\[
2x + 46 = 7x + 6
\]
2. Solve the equation for \( x \):
\[
2x + 46 = 7x + 6
\]
\[
46 - 6 = 7x - 2x
\]
\[
40 = 5x
\]
\[
x = 8
\]
3. Substitute \( x = 8 \) back into either angle expression to find the angle measure:
\[
(2x + 46)^\circ = (2(8) + 46)^\circ = (16 + 46)^\circ = 62^\circ
\]
**Answer:**
The measure of the angles is 62 degrees.
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