△LMN is isosceles, with ∠M≅∠L and m∠L=36° . What are the measures of angles M and N ?
Since ∠M≅∠L and ∠L=36°, then ∠M=36°.
Since ∆LMN is isosceles, ∠L≅∠N.
Therefore, ∠N=36°.
your missing m∠M
Apologies for the oversight.
Since ∆LMN is isosceles, ∠L≅∠N. Let's denote m∠N as x.
Therefore, ∠L=36° and ∠N=x.
Since the sum of the internal angles in a triangle is 180°, we can write the equation:
∠M + ∠L + ∠N = 180°
Substituting the given values, we have:
36° + 36° + x = 180°
Simplifying the equation, we find:
2(36°) + x = 180°
72° + x = 180°
Subtracting 72° from both sides:
x = 108°
Hence, the measures of angles M, L, and N are 36°, 36°, and 108° respectively.
and m∠N
Apologies for the confusion.
Given that ∆LMN is isosceles and ∠L=36°, we know that ∠M=36° as well.
Since the sum of the internal angles in a triangle is 180°, we have:
∠L + ∠M + ∠N = 180°
Substituting the known values, we get:
36° + 36° + ∠N = 180°
Simplifying the equation, we find:
72° + ∠N = 180°
Subtracting 72° from both sides:
∠N = 180° - 72°
∠N = 108°
Hence, the measures of angles M and N are both 36°, and the measure of angle N is 108°.