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Solve for x. Round to the nearest tenth of a degree, if necessary. C 45 35 A

Solve for x. Round to the nearest tenth of a degree, if necessary. C 45 35 A

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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### Geometry Problem: Solving for Angle \( x \) **Problem Statement:** Solve for \( x \). Round to the nearest tenth of a degree, if necessary. **Diagram Description:** - The diagram represents a right triangle \( ABC \). - Vertex \( B \) is the right angle. - Angle \( A \) is unknown and labeled as \( x \) degrees. - Angle \( C \) is given as 45 degrees. - The other angle adjacent to the right angle \( B \) is given as 35 degrees. **Concepts Applied:** 1. In any triangle, the sum of the interior angles is always 180 degrees. 2. In a right triangle, one of those angles is always 90 degrees. **Steps to Solve:** Given: - Angle \( C \) = 45 degrees - Angle \( B \) = 90 degrees (since it is a right triangle) - Angle \( A \) = \( x \) According to the property of triangles: \[ \text{Sum of angles in }\triangle ABC = 180^\circ \] Therefore, \[ x + 35^\circ + 45^\circ = 180^\circ \] Simplify the equation: \[ x + 80^\circ = 180^\circ \] \[ x = 180^\circ - 80^\circ \] \[ x = 100^\circ \] So, \[ x = 100 \text{ degrees} \] Since the problem requires the angle to be rounded to the nearest tenth, and \( 100.0 \) degrees is already at a tenth, \( x = 100.0 \) degrees. **Conclusion:** The unknown angle \( x \) in triangle \( ABC \) is 100.0 degrees.
Transcribed Image Text:### Geometry Problem: Solving for Angle \( x \) **Problem Statement:** Solve for \( x \). Round to the nearest tenth of a degree, if necessary. **Diagram Description:** - The diagram represents a right triangle \( ABC \). - Vertex \( B \) is the right angle. - Angle \( A \) is unknown and labeled as \( x \) degrees. - Angle \( C \) is given as 45 degrees. - The other angle adjacent to the right angle \( B \) is given as 35 degrees. **Concepts Applied:** 1. In any triangle, the sum of the interior angles is always 180 degrees. 2. In a right triangle, one of those angles is always 90 degrees. **Steps to Solve:** Given: - Angle \( C \) = 45 degrees - Angle \( B \) = 90 degrees (since it is a right triangle) - Angle \( A \) = \( x \) According to the property of triangles: \[ \text{Sum of angles in }\triangle ABC = 180^\circ \] Therefore, \[ x + 35^\circ + 45^\circ = 180^\circ \] Simplify the equation: \[ x + 80^\circ = 180^\circ \] \[ x = 180^\circ - 80^\circ \] \[ x = 100^\circ \] So, \[ x = 100 \text{ degrees} \] Since the problem requires the angle to be rounded to the nearest tenth, and \( 100.0 \) degrees is already at a tenth, \( x = 100.0 \) degrees. **Conclusion:** The unknown angle \( x \) in triangle \( ABC \) is 100.0 degrees.
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