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
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**Angle Terminology with Equations**
\(\angle A\) and \(\angle B\) are supplementary angles. If \( m\angle A = (5x + 27) \) and \( m\angle B = (5x - 7) \), then find the measure of \(\angle A\).
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Explanation:
- **Supplementary Angles:** Two angles are supplementary if the sum of their measures is \(180^\circ\).
To solve for the measure of \(\angle A\), we can set up the following equation based on the given information:
\[ (5x + 27) + (5x - 7) = 180 \]
\[ 5x + 5x + 27 - 7 = 180 \]
\[ 10x + 20 = 180 \]
\[ 10x = 160 \]
\[ x = 16 \]
Now, substitute back to find the measure of \(\angle A\):
\[ m\angle A = 5x + 27 \]
\[ m\angle A = 5(16) + 27 \]
\[ m\angle A = 80 + 27 \]
\[ m\angle A = 107^\circ \]
Thus, the measure of \(\angle A\) is \(107^\circ\).
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This section falls under the geometry or trigonometry category and could be useful for high school level mathematics or standardized test prep.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76fe98d6-642d-4ca9-9396-ce0e2c923c57%2F31eb6c26-dce6-41ad-aea7-e018170ed69e%2Fdogjgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Angle Terminology with Equations**
\(\angle A\) and \(\angle B\) are supplementary angles. If \( m\angle A = (5x + 27) \) and \( m\angle B = (5x - 7) \), then find the measure of \(\angle A\).
---
Explanation:
- **Supplementary Angles:** Two angles are supplementary if the sum of their measures is \(180^\circ\).
To solve for the measure of \(\angle A\), we can set up the following equation based on the given information:
\[ (5x + 27) + (5x - 7) = 180 \]
\[ 5x + 5x + 27 - 7 = 180 \]
\[ 10x + 20 = 180 \]
\[ 10x = 160 \]
\[ x = 16 \]
Now, substitute back to find the measure of \(\angle A\):
\[ m\angle A = 5x + 27 \]
\[ m\angle A = 5(16) + 27 \]
\[ m\angle A = 80 + 27 \]
\[ m\angle A = 107^\circ \]
Thus, the measure of \(\angle A\) is \(107^\circ\).
---
This section falls under the geometry or trigonometry category and could be useful for high school level mathematics or standardized test prep.
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