△LMN is isosceles, with ∠M≅∠L and m∠L=36°. What are the measures of angles M and N
To find the measures of angles M and N in the isosceles triangle LMN, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Given that ∠M ≅ ∠L and m∠L = 36°, it means that angle L is the same as angle M, and angle L measures 36 degrees.
Let's find the measure of angle N using the fact that the sum of the angles in a triangle is 180 degrees.
Step 1: Find the total measure of angles in a triangle
The sum of the measures of angles in a triangle is 180 degrees.
Step 2: Find the measure of angle L
Given that m∠L = 36°, we know that angle L measures 36 degrees.
Step 3: Find the measure of angle M
Since angle M and angle L are congruent (≅), angle M also measures 36 degrees.
Step 4: Find the measure of angle N
Substitute the values of angles L and M into the equation that sums up the measures of angles in a triangle, and solve for angle N:
180 = 36 + 36 + angle N
180 = 72 + angle N
angle N = 180 - 72
angle N = 108 degrees
Therefore, the measures of angles M and N are:
m∠M = 36°
m∠N = 108°
Since ∠M ≅ ∠L and LMN is isosceles, then ∠L ≅ ∠N.
Since the sum of the measures of the angles in a triangle is 180°, we have:
∠L + ∠M + ∠N = 180°
36° + ∠M + ∠L = 180°
2∠L + ∠M = 180°
2(36°) + ∠M = 180°
72° + ∠M = 180°
∠M = 180° - 72°
∠M = 108°
Since ∠M ≅ ∠L, then ∠L = 108° as well.
Since LMN is isosceles and ∠L ≅ ∠N, then ∠N = 108° as well.
So, the measure of angle M is 108° and the measure of angle N is 108°.