Given a triangle with angles [tex]\( 32^\circ \)[/tex], [tex]\( 53^\circ \)[/tex], and [tex]\( 95^\circ \)[/tex], we need to determine how these angles are assigned to [tex]\( \angle A \)[/tex], [tex]\( \angle B \)[/tex], and [tex]\( \angle C \)[/tex] based on the side lengths of the triangle.
Let's examine the fact that in any triangle, the longest side is opposite the largest angle. Thus, the angle with the largest measure will be opposite the side with the largest length.
1. Identify the largest angle:
- Among [tex]\( 32^\circ \)[/tex], [tex]\( 53^\circ \)[/tex], and [tex]\( 95^\circ \)[/tex], the largest angle is [tex]\( 95^\circ \)[/tex].
2. Assign [tex]\( 95^\circ \)[/tex] to one of the angles:
- Since [tex]\( 95^\circ \)[/tex] is the largest angle, it must be opposite the longest side. We can assign [tex]\( m \angle A = 95^\circ \)[/tex].
3. Identify the next largest angle:
- After [tex]\( 95^\circ \)[/tex], the next largest angle is [tex]\( 53^\circ \)[/tex].
4. Assign [tex]\( 53^\circ \)[/tex] to another one of the angles:
- Since [tex]\( 53^\circ \)[/tex] is the next largest angle, it must be opposite the side which is shorter than the longest side but longer than the shortest side. We can assign [tex]\( m \angle B = 53^\circ \)[/tex].
5. Assign the smallest angle to the remaining angle:
- The smallest angle, [tex]\( 32^\circ \)[/tex], must therefore be opposite the shortest side. We can assign [tex]\( m \angle C = 32^\circ \)[/tex].
So, the measures of the angles based on their side lengths are:
[tex]\[ m \angle A = 95^\circ, \quad m \angle B = 53^\circ, \quad m \angle C = 32^\circ \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{m \angle A=95^{\circ}, m \angle B=53^{\circ}, m \angle C=32^{\circ}} \][/tex]
