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]
