Question

Question
△LMN
is isosceles, with ∠M≅∠L
and m∠L=36°
. What are the measures of angles M
and N
?(1 point)
m∠M =

°
and m∠N =

°

Answer 1

In triangle \( \triangle LMN \), since it is isosceles with \( \angle M \cong \angle L \) and \( m\angle L = 36^\circ \), we have:

\[
m\angle M = m\angle L = 36^\circ
\]

Next, we use the fact that the sum of the angles in a triangle is \( 180^\circ \):

\[
m\angle L + m\angle M + m\angle N = 180^\circ
\]

Substituting the known values:

\[
36^\circ + 36^\circ + m\angle N = 180^\circ
\]

This simplifies to:

\[
72^\circ + m\angle N = 180^\circ
\]

To find \( m\angle N \), we subtract \( 72^\circ \) from \( 180^\circ \):

\[
m\angle N = 180^\circ - 72^\circ = 108^\circ
\]

Thus, the measures of the angles are:

\[
m\angle M = 36^\circ \quad \text{and} \quad m\angle N = 108^\circ
\]