△LMN is isosceles, with ∠M≅∠L and m∠L=36° . What are the measures of angles M and N ?(1 point)
no M is 36
108
Since △LMN is isosceles with ∠M≅∠L, then it follows that ∠N≅∠M. Since the sum of the angles in any triangle is 180°, we have:
m∠L + m∠M + m∠N = 180°
Substituting the given value of m∠L = 36°, and using the fact that ∠N≅∠M:
36° + m∠M + m∠M = 180°
2m∠M = 180° - 36°
2m∠M = 144°
Dividing both sides of the equation by 2:
m∠M = 72°
Since ∠M≅∠L, m∠L = 72°.
And since the sum of the angles in a triangle is 180°:
m∠N = 180° - m∠L - m∠M
m∠N = 180° - 72° - 72°
m∠N = 36°
Therefore, the measures of angles M and N are 72° and 36°, respectively.
nope ur wrong
Apologies for the error in the previous response. Let's correct it:
Since △LMN is isosceles with ∠M ≅ ∠L, it means that angles M and N are equal in measure. Let's denote the measure of ∠M and ∠N as x.
Given that m∠L = 36°, we can use the fact that the sum of angles in a triangle is 180°:
m∠L + m∠M + m∠N = 180°
Substituting the given value of m∠L = 36°, and using the fact that angles M and N are equal:
36° + x + x = 180°
Combine like terms:
36° + 2x = 180°
Now, solve for x:
2x = 180° - 36°
2x = 144°
Dividing both sides of the equation by 2:
x = 144°/2
x = 72°
Therefore, the measures of angles M and N are both 72°.
Apologies for the confusion.
If ∠L is 36° and ∠M is congruent to ∠L, then ∠M is also 36°.
Since ∠M and ∠L are congruent, it follows that angles M and L are also congruent. Therefore, the measures of angles M and L are both 36°.
And since △LMN is isosceles, ∠N is also congruent to ∠M and ∠L. Thus, the measure of angle N is also 36°.
Therefore, the measures of angles M and N are both 36°.