Answer :
To determine the correct measures of the angles for the given triangle based on side lengths, we start by identifying the sum of the internal angles of any triangle, which is always [tex]\(180^\circ\)[/tex]. The measures of the angles are provided as [tex]\(32^\circ, 53^\circ\)[/tex], and [tex]\(95^\circ\)[/tex], confirming that these angles form a valid triangle:
[tex]\[ 32^\circ + 53^\circ + 95^\circ = 180^\circ \][/tex]
With this information in mind, we need to match the angles [tex]\(32^\circ, 53^\circ\)[/tex], and [tex]\(95^\circ\)[/tex] to the correct options for [tex]\( \angle A \)[/tex], [tex]\( \angle B \)[/tex], and [tex]\( \angle C \)[/tex].
Given the correct measures for angle [tex]\( A \)[/tex], angle [tex]\( B \)[/tex], and angle [tex]\( C \)[/tex]:
[tex]\[ m \angle A = 32^\circ \][/tex]
[tex]\[ m \angle B = 53^\circ \][/tex]
[tex]\[ m \angle C = 95^\circ \][/tex]
Therefore, the correct option is:
[tex]\[ m \angle A = 32^\circ, m \angle B = 53^\circ, m \angle C = 95^\circ \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
The correct order based on the given angles is [tex]\( m \angle A = 32^\circ, m \angle B = 53^\circ, m \angle C = 95^\circ \)[/tex], which corresponds to option 2.
[tex]\[ 32^\circ + 53^\circ + 95^\circ = 180^\circ \][/tex]
With this information in mind, we need to match the angles [tex]\(32^\circ, 53^\circ\)[/tex], and [tex]\(95^\circ\)[/tex] to the correct options for [tex]\( \angle A \)[/tex], [tex]\( \angle B \)[/tex], and [tex]\( \angle C \)[/tex].
Given the correct measures for angle [tex]\( A \)[/tex], angle [tex]\( B \)[/tex], and angle [tex]\( C \)[/tex]:
[tex]\[ m \angle A = 32^\circ \][/tex]
[tex]\[ m \angle B = 53^\circ \][/tex]
[tex]\[ m \angle C = 95^\circ \][/tex]
Therefore, the correct option is:
[tex]\[ m \angle A = 32^\circ, m \angle B = 53^\circ, m \angle C = 95^\circ \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
The correct order based on the given angles is [tex]\( m \angle A = 32^\circ, m \angle B = 53^\circ, m \angle C = 95^\circ \)[/tex], which corresponds to option 2.
