△LMN is isosceles, with ∠M≅∠L and m∠L=36° . What are the measures of angles M and N ?
m∠M =[ ]° , and m∠N =[ ]°
Since ∠M≅∠L, we have m∠M = 36° as well.
Since ∠L+∠M+∠N = 180° (sum of angles in a triangle), we can substitute the given values:
36° + 36° + ∠N = 180°
Simplifying the equation:
72° + ∠N = 180°
Subtracting 72° from both sides:
∠N = 180° - 72°
∠N = 108°
So, the measures of angles M and N are:
m∠M = 36°
m∠N = 108°