### Problem Statement#### Solve for \( x \):10. ![Triangle diagram](https://via.placeholder.com/15) - \( \angle BAC = (2x + 8)^\circ \) - \( \angle ABC = (3x - 5)^\circ \) \( \overline{AB} \) is an altitude of the triangle.### Explanation of DiagramIn the given diagram, there is a triangle labeled \( \triangle ABC \). The point \( A \) is the apex of the triangle, while \( B \) is located at the base middle point. Line segment \( \overline{AB} \) represents the altitude of the triangle, dropping perpendicular from \( A \) to \( B \). The angles in the triangle are as follows:- Angle \( BAC \) is given by \( (2x + 8)^\circ \).- Angle \( ABC \) is given by \( (3x - 5)^\circ \).The altitude \( \overline{AB} \) indicates that it splits the triangle into two right-angled triangles. Thus, the angles formed by \( \overline{AB} \) and the base of the triangle are right angles.### ObjectiveYou are required to solve for \( x \).### Solution Approach1. **Using Triangle Properties:** Since \( \overline{AB} \) is the altitude, it splits the triangle into two right-angled triangles, where one angle at the base \( \angle ABC \) and the other at the base opposite \( \angle BAC \) must sum up to \( 90^\circ \).2. **Equation Setup:** \[ (2x + 8)^\circ + (3x - 5)^\circ = 90^\circ \]3. **Solving the Equation:** \[ 2x + 8 + 3x - 5 = 90 \] Simplify and solve for \( x \). \[ 5x + 3 = 90 \] \[ 5x = 87 \] \[ x = 17.4 \]Therefore, the value of \( x \) that satisfies the given conditions is \( 17.4 \).

Answered: Image /qna-images/answer/a82ea849-82ba-40da-93df-6b6e95904c5e.jpg

Answered: 10. 2x+8)° (3x-5)° B

10. 2x+8)° (3x-5)° B

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