△LMN is isosceles, with ∠M≅∠L and m∠L=36°. What are the measures of angles M and N?(1 point)
Since ∠M ≅ ∠L and ∠L = 36°, we know that ∠M = 36°.
Since ∆LMN is isosceles, angles L and M are congruent, which means ∠N = ∠M = 36°.
Therefore, the measures of angles M and N are both 36°.
If ∠M ≅ ∠L in an isosceles triangle △LMN, it means that angle M and angle N are congruent. Let's denote the measure of angles M and N as x degrees.
Given that the measure of angle L is 36 degrees, we can set up an equation:
x + x + 36 = 180 (sum of angles in a triangle is 180 degrees)
Simplifying the equation:
2x + 36 = 180
Subtracting 36 from both sides:
2x = 144
Dividing both sides by 2:
x = 72
Therefore, the measure of angle M is 72 degrees, and the measure of angle N is also 72 degrees.