To determine the correct measures of the angles [tex]\( \angle A \)[/tex], [tex]\( \angle B \)[/tex], and [tex]\( \angle C \)[/tex] in the triangle:
1. We are given three angles: [tex]\( 32^{\circ} \)[/tex], [tex]\( 53^{\circ} \)[/tex], and [tex]\( 95^{\circ} \)[/tex].
2. We need to check the provided options and match the given angles with the measures:
- Option 1: [tex]\( m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ} \)[/tex]
- Option 2: [tex]\( m \angle A=32^{\circ}, m \angle B=53^{\circ}, m \angle C=95^{\circ} \)[/tex]
- Option 3: [tex]\( m \angle A=43^{\circ}, m \angle B=32^{\circ}, m \angle C=95^{\circ} \)[/tex]
- Option 4: [tex]\( m \angle A=53^{\circ}, m \angle B=95^{\circ}, m \angle C=32^{\circ} \)[/tex]
3. Let's focus on the angle measures themselves:
- [tex]\( \angle A = 95^{\circ} \)[/tex]: This angle appears only in options 1 and 4 for [tex]\( \angle A \)[/tex] and option 2 for [tex]\( \angle C \)[/tex].
- [tex]\( \angle B = 53^{\circ} \)[/tex]: This angle appears in all options, but with different labels.
- [tex]\( \angle C = 32^{\circ} \)[/tex]: This angle appears in all options except option 3.
4. Considering the triangle angle sum property (sum of angles = [tex]\( 180^{\circ} \)[/tex]):
- [tex]\( m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ} \)[/tex]
Therefore, the correct measures based on the given angles would be:
[tex]\[ m \angle A = 95^{\circ}, m \angle B = 53^{\circ}, m \angle C = 32^{\circ} \][/tex]
So the correct answer is:
[tex]\[ \boxed{m \angle A = 95^{\circ}, m \angle B = 53^{\circ}, m \angle C = 32^{\circ}} \][/tex]
