oliviarubinstein0
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Consider the triangle.

The measures of the angles of the triangle are [tex]\(32^{\circ}, 53^{\circ}, 95^{\circ}\)[/tex]. Based on the side lengths, what are the measures of each angle?

A. [tex]\(m \angle A = 95^{\circ}, m \angle B = 53^{\circ}, m \angle C = 32^{\circ}\)[/tex]

B. [tex]\(m \angle A = 32^{\circ}, m \angle B = 53^{\circ}, m \angle C = 95^{\circ}\)[/tex]

C. [tex]\(m \angle A = 43^{\circ}, m \angle B = 32^{\circ}, m \angle C = 95^{\circ}\)[/tex]

D. [tex]\(m \angle A = 53^{\circ}, m \angle B = 95^{\circ}, m \angle C = 32^{\circ}\)[/tex]

Sagot :

GinnyAnswer
To solve this problem, let's analyze the given information and match the angles of the triangle to the given choices.

The angles specified for the triangle are [tex]\(32^{\circ}, 53^{\circ},\)[/tex] and [tex]\(95^{\circ}\)[/tex].

Given the choices:
1. [tex]\( m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ} \)[/tex]
2. [tex]\( m \angle A=32^{\circ}, m \angle B=53^{\circ}, m \angle C=95^{\circ} \)[/tex]
3. [tex]\( m \angle A=43^{\circ}, m \angle B=32^{\circ}, m \angle C=95^{\circ} \)[/tex]
4. [tex]\( m \angle A=53^{\circ}, m \angle B=95^{\circ}, m \angle C=32^{\circ} \)[/tex]

We need to determine which set corresponds to the correct arrangement of the given angles [tex]\(32^{\circ}, 53^{\circ},\)[/tex] and [tex]\(95^{\circ}\)[/tex].

By verifying the sets:

1. [tex]\( m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ} \)[/tex]:
- [tex]\( \angle A = 95^{\circ} \)[/tex]
- [tex]\( \angle B = 53^{\circ} \)[/tex]
- [tex]\( \angle C = 32^{\circ} \)[/tex]

This set matches the given angles.

2. [tex]\( m \angle A=32^{\circ}, m \angle B=53^{\circ}, m \angle C=95^{\circ} \)[/tex]:
- [tex]\( \angle A = 32^{\circ} \)[/tex]
- [tex]\( \angle B = 53^{\circ} \)[/tex]
- [tex]\( \angle C = 95^{\circ} \)[/tex]

This set also matches the given angles but with different assignment to the variables.

3. [tex]\( m \angle A=43^{\circ}, m \angle B=32^{\circ}, m \angle C=95^{\circ} \)[/tex]:
- [tex]\( \angle A = 43^{\circ} \)[/tex]
- [tex]\( \angle B = 32^{\circ} \)[/tex]
- [tex]\( \angle C = 95^{\circ} \)[/tex]

This set has one angle that does not match the given angles.

4. [tex]\( m \angle A=53^{\circ}, m \angle B=95^{\circ}, m \angle C=32^{\circ} \)[/tex]:
- [tex]\( \angle A = 53^{\circ} \)[/tex]
- [tex]\( \angle B = 95^{\circ} \)[/tex]
- [tex]\( \angle C = 32^{\circ} \)[/tex]

This set swaps [tex]\(53^{\circ}\)[/tex] with [tex]\(95^{\circ}\)[/tex], not matching the correct assignment.

By comparing all the options, the set:
[tex]\[ m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ} \][/tex]
finds to match correctly.

Hence, the correct choice is:

[tex]\[ \boxed{m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ}} \][/tex]
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