△LMN is isosceles, with ∠M≌∠L and m∠L = 36º. What are the measures of angles M and N?
m∠M = __ º and m∠N = __º
In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.
Given that ∠L = 36º and ∠M ≌ ∠L, we know that ∠M = ∠L = 36º.
Since the sum of the angles in a triangle is 180º, we can find ∠N.
∠L + ∠M + ∠N = 180º
36º + 36º + ∠N = 180º
72º + ∠N = 180º
Subtract 72º from both sides:
∠N = 180º - 72º
∠N = 108º
Therefore, m∠M = 36º and m∠N = 108º.