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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Question
![**Problem Statement:**
A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of \( x \).
**Diagram Description:**
The provided diagram shows a right triangle with one angle marked as a right angle (90°). One of the sides of the triangle has been extended to form an exterior angle of 128°. The interior angle adjacent to the exterior angle is marked as \( x \).
**Mathematical Explanation:**
To solve for \( x \), we can use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. However, in this case, since the exterior angle and the adjacent interior angle are on a straight line, they are supplementary.
Therefore:
\[ x + 128^\circ = 180^\circ \]
\[ x = 180^\circ - 128^\circ \]
\[ x = 52^\circ \]
**Answer:**
\[ x = \boxed{52^\circ} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F420be1ed-4800-494b-a602-370b9d863128%2F8f2495ee-89ba-400d-962a-c3c5578a90de%2Fv7a4yub_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 128°. Find the value of \( x \).
**Diagram Description:**
The provided diagram shows a right triangle with one angle marked as a right angle (90°). One of the sides of the triangle has been extended to form an exterior angle of 128°. The interior angle adjacent to the exterior angle is marked as \( x \).
**Mathematical Explanation:**
To solve for \( x \), we can use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. However, in this case, since the exterior angle and the adjacent interior angle are on a straight line, they are supplementary.
Therefore:
\[ x + 128^\circ = 180^\circ \]
\[ x = 180^\circ - 128^\circ \]
\[ x = 52^\circ \]
**Answer:**
\[ x = \boxed{52^\circ} \]
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