To determine the correct measure of each angle in the given triangle, we need to match the provided options with the given angles. The angles given are [tex]\(32^\circ\)[/tex], [tex]\(53^\circ\)[/tex], and [tex]\(95^\circ\)[/tex].
Let's compare each option with the given angles:
1. Option 1:
[tex]\[
m \angle A = 95^\circ, \quad m \angle B = 53^\circ, \quad m \angle C = 32^\circ
\][/tex]
This option matches the given angles.
2. Option 2:
[tex]\[
m \angle A = 32^\circ, \quad m \angle B = 53^\circ, \quad m \angle C = 95^\circ
\][/tex]
This option also matches the given angles.
3. Option 3:
[tex]\[
m \angle A = 43^\circ, \quad m \angle B = 32^\circ, \quad m \angle C = 95^\circ
\][/tex]
This option does not match the given angles as [tex]\(43^\circ\)[/tex] is not one of the given angles.
4. Option 4:
[tex]\[
m \angle A = 53^\circ, \quad m \angle B = 95^\circ, \quad m \angle C = 32^\circ
\][/tex]
This option again matches the given angles.
So, the measures of each angle in the triangle based on the side lengths can be summarized as:
- [tex]\(m \angle A = 95^\circ\)[/tex], [tex]\(m \angle B = 53^\circ\)[/tex], [tex]\(m \angle C = 32^\circ\)[/tex]
- [tex]\(m \angle A = 32^\circ\)[/tex], [tex]\(m \angle B = 53^\circ\)[/tex], [tex]\(m \angle C = 95^\circ\)[/tex]
- [tex]\(m \angle A = 53^\circ\)[/tex], [tex]\(m \angle B = 95^\circ\)[/tex], [tex]\(m \angle C = 32^\circ\)[/tex]
These match the options:
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]
4. [tex]\(m \angle A = 53^\circ, m \angle B = 95^\circ, m \angle C = 32^\circ\)[/tex]
Option 3 is incorrect.
Thus, the correct angle measures consistent with the given angles are options 1, 2, and 4.
