Question

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

Answer 1

Given that triangle \( \triangle LMN \) is isosceles with \( \angle M \cong \angle L \) and \( m\angle L = 36^\circ \), we know that:

1. Since \( \angle M \cong \angle L \), it follows that \( m\angle M = m\angle L = 36^\circ \).

2. The sum of the angles in any triangle is \( 180^\circ \). Therefore, we have:

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

Substituting the values we know:

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

This simplifies to:

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

To find \( m\angle N \), subtract \( 72^\circ \) from both sides:

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

Thus, the measures of the angles are:

- \( m\angle M = 36^\circ \)
- \( m\angle L = 36^\circ \)
- \( m\angle N = 108^\circ \)