### 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°

Answered: Image /qna-images/answer/bd07082c-ab2f-4030-96ce-4cca55d45256.jpg

Answered: 32 H M In isosceles AHAM, mA = 32°,.…

Math

Geometry

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

Problem 1CT

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

### 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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