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Find the measure of angle A. 5) x + 53 x+56 87° A

Find the measure of angle A. 5) x + 53 x+56 87° 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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Find the measure of A

### Problem Statement **Find the measure of angle A.** #### Diagram: There is a triangle labeled with angles and expressions: - **Angle A:** The measure of angle A is not given and is to be found. - **Second angle:** Labeled as \( x + 56 \). - **Third angle:** Labeled as \( x + 53 \). - **Fourth angle:** Given as \( 87^\circ \). ### Explanation To find the measure of angle A, use the triangle angle sum property, which states the sum of the angles in a triangle is \(180^\circ\). **Equation:** \[ A + (x + 56) + (x + 53) + 87 = 180 \] **Solve for A:** 1. Combine like terms: \[ A + 2x + 196 = 180 \] 2. Simplify and isolate \( A \): \[ A = 180 - 2x - 196 \] \[ A = -2x - 16 \] Thus, find \( x \) using additional properties or information if required, and substitute back to find \( A \). However, further steps depend on additional equations or values for \( x \).
Transcribed Image Text:### Problem Statement **Find the measure of angle A.** #### Diagram: There is a triangle labeled with angles and expressions: - **Angle A:** The measure of angle A is not given and is to be found. - **Second angle:** Labeled as \( x + 56 \). - **Third angle:** Labeled as \( x + 53 \). - **Fourth angle:** Given as \( 87^\circ \). ### Explanation To find the measure of angle A, use the triangle angle sum property, which states the sum of the angles in a triangle is \(180^\circ\). **Equation:** \[ A + (x + 56) + (x + 53) + 87 = 180 \] **Solve for A:** 1. Combine like terms: \[ A + 2x + 196 = 180 \] 2. Simplify and isolate \( A \): \[ A = 180 - 2x - 196 \] \[ A = -2x - 16 \] Thus, find \( x \) using additional properties or information if required, and substitute back to find \( A \). However, further steps depend on additional equations or values for \( x \).
The image contains diagrams of two right triangles labeled as questions 6 and 8. ### Triangle for Question 6: - The triangle is labeled with vertices and sides as follows: - The vertex labeled 'A' forms the top point of the triangle. - The side adjacent to the right angle is labeled \(7x + 11\). - The side opposite the right angle and leading to point 'A' is labeled \(3x + 9\). ### Triangle for Question 8: - This triangle is another right triangle with sides labeled: - One side is labeled \(13x\). - The hypotenuse is labeled \(5x\). These triangles appear to be part of a geometry exercise, likely involving the Pythagorean theorem or solving for \(x\) using algebraic equations.
Transcribed Image Text:The image contains diagrams of two right triangles labeled as questions 6 and 8. ### Triangle for Question 6: - The triangle is labeled with vertices and sides as follows: - The vertex labeled 'A' forms the top point of the triangle. - The side adjacent to the right angle is labeled \(7x + 11\). - The side opposite the right angle and leading to point 'A' is labeled \(3x + 9\). ### Triangle for Question 8: - This triangle is another right triangle with sides labeled: - One side is labeled \(13x\). - The hypotenuse is labeled \(5x\). These triangles appear to be part of a geometry exercise, likely involving the Pythagorean theorem or solving for \(x\) using algebraic equations.
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