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 Statement
A side of the triangle below has been extended to form an exterior angle of \(133^\circ\). Find the value of \(x\).
### Diagram Explanation
The diagram illustrates a triangle with one of its sides extended to form an exterior angle. In the triangle:
- One interior angle is \(21^\circ\).
- The extended exterior angle adjacent to the interior angle \(x^\circ\) is \(133^\circ\).
### Diagram Description
- The triangle includes one marked internal angle \(21^\circ\).
- The vertex opposite the \(21^\circ\) internal angle has an angle marked as \(x^\circ\).
- The side is extended at this internal angle to form an exterior angle of \(133^\circ\).
### Question
**Answer:**
\[ x = \_\_\_ \]
### Solution Explanation (Optional)
To solve for \(x\):
1. Recognize that the exterior angle \(133^\circ\) is the sum of the two non-adjacent interior angles.
2. Use the equation:
\[ 133^\circ = 21^\circ + x^\circ \]
3. Subtract \(21^\circ\) from \(133^\circ\):
\[ x^\circ = 133^\circ - 21^\circ = 112^\circ \]
Therefore:
\[ \boxed{112^\circ} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F760f95d1-2d5a-40a7-a35b-0c4fdbdfef12%2Fbcb25253-7829-488a-8932-eeed39755fb7%2F7qrcgin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A side of the triangle below has been extended to form an exterior angle of \(133^\circ\). Find the value of \(x\).
### Diagram Explanation
The diagram illustrates a triangle with one of its sides extended to form an exterior angle. In the triangle:
- One interior angle is \(21^\circ\).
- The extended exterior angle adjacent to the interior angle \(x^\circ\) is \(133^\circ\).
### Diagram Description
- The triangle includes one marked internal angle \(21^\circ\).
- The vertex opposite the \(21^\circ\) internal angle has an angle marked as \(x^\circ\).
- The side is extended at this internal angle to form an exterior angle of \(133^\circ\).
### Question
**Answer:**
\[ x = \_\_\_ \]
### Solution Explanation (Optional)
To solve for \(x\):
1. Recognize that the exterior angle \(133^\circ\) is the sum of the two non-adjacent interior angles.
2. Use the equation:
\[ 133^\circ = 21^\circ + x^\circ \]
3. Subtract \(21^\circ\) from \(133^\circ\):
\[ x^\circ = 133^\circ - 21^\circ = 112^\circ \]
Therefore:
\[ \boxed{112^\circ} \]
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