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A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of x.

A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of x.

Elementary Geometry For College Students, 7e
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:** \[ x = \boxed{52^\circ} \]
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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