32 H M In isosceles AHAM, mA = 32°,. What is m/H? 32 O 58" O 74° O 148°

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
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### Isosceles Triangle Angle Calculation

#### Problem Statement:

Given isosceles triangle △HAM where the vertex angle, ∠A, is 32°:

1. Determine the measure of ∠H.

#### Diagram Description:

- The diagram depicts an isosceles triangle △HAM.
- Point A is the vertex.
- Side HA is congruent to side MA.
- The vertex angle, ∠A, is marked as 32°.

#### Question:

What is the measure of ∠H?

#### Multiple Choice Options:

- A. 32°
- B. 58°
- C. 74°
- D. 148°

#### Explanation:

In an isosceles triangle, the base angles are congruent. Let's denote the measure of ∠H and ∠M as x.

1. The sum of angles in a triangle is 180°.
2. Since △HAM is isosceles, ∠H = ∠M = x.
3. The equation is: 
   - 32° (vertex angle) + x + x = 180°
   - 32° + 2x = 180°
   - 2x = 148°
   - x = 74°

Thus, the measure of ∠H is 74°.

#### Answer:
- C. 74°
Transcribed Image Text:### Isosceles Triangle Angle Calculation #### Problem Statement: Given isosceles triangle △HAM where the vertex angle, ∠A, is 32°: 1. Determine the measure of ∠H. #### Diagram Description: - The diagram depicts an isosceles triangle △HAM. - Point A is the vertex. - Side HA is congruent to side MA. - The vertex angle, ∠A, is marked as 32°. #### Question: What is the measure of ∠H? #### Multiple Choice Options: - A. 32° - B. 58° - C. 74° - D. 148° #### Explanation: In an isosceles triangle, the base angles are congruent. Let's denote the measure of ∠H and ∠M as x. 1. The sum of angles in a triangle is 180°. 2. Since △HAM is isosceles, ∠H = ∠M = x. 3. The equation is: - 32° (vertex angle) + x + x = 180° - 32° + 2x = 180° - 2x = 148° - x = 74° Thus, the measure of ∠H is 74°. #### Answer: - C. 74°
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