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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![**Problem 8: Finding the Value of \( x \)**
**Diagram Description:**
The diagram consists of a circle divided into three sectors by two radii and a line segment that is not a radius. Each segment forms an angle at the center of the circle. The angles inside the circle are as follows:
- One angle is \( 80^\circ \).
- Another angle is \( 94^\circ \).
- The third angle is labeled as \( x \), which we need to find.
**Problem Statement:**
Find the value of \( x \).
**Solution Explanation:**
In a circle, the sum of the angles around a point is \( 360^\circ \). Therefore, we can set up the equation as follows:
\[ 80^\circ + 94^\circ + x = 360^\circ \]
Solving for \( x \):
\[ x = 360^\circ - (80^\circ + 94^\circ) \]
\[ x = 360^\circ - 174^\circ \]
\[ x = 186^\circ \]
Thus, the value of \( x \) is \( 186^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42779bdc-66e8-47e8-8a59-0cd69b39b8c3%2F37eaf7de-c8af-4f86-8c56-b3e62fd1cc32%2Fgoru9qf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 8: Finding the Value of \( x \)**
**Diagram Description:**
The diagram consists of a circle divided into three sectors by two radii and a line segment that is not a radius. Each segment forms an angle at the center of the circle. The angles inside the circle are as follows:
- One angle is \( 80^\circ \).
- Another angle is \( 94^\circ \).
- The third angle is labeled as \( x \), which we need to find.
**Problem Statement:**
Find the value of \( x \).
**Solution Explanation:**
In a circle, the sum of the angles around a point is \( 360^\circ \). Therefore, we can set up the equation as follows:
\[ 80^\circ + 94^\circ + x = 360^\circ \]
Solving for \( x \):
\[ x = 360^\circ - (80^\circ + 94^\circ) \]
\[ x = 360^\circ - 174^\circ \]
\[ x = 186^\circ \]
Thus, the value of \( x \) is \( 186^\circ \).
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