Question

Suppose that LMN is isosceles with base ML

Answer 1

Answer:

m∠M = 54°

m∠N = 72°

m∠L = 54°

Step-by-step explanation:

In the figure attached,

ΔLMN is an isosceles triangle having sides MN ≅ NL

Therefore, angles opposite to these sides will be equal in measure.

m∠M ≅ m∠L ≅ (2x + 36)°

Since, m∠M + m∠N + m∠L = 180°

(2x + 36)° + (5x + 27)° + (2x + 36)° = 180°

9x + 99 = 180

9x = 180 - 99

x = $\frac{81}{9}$

x = 9

Therefore, m∠L = m∠M = (2x + 36)° = (2×9) + 36

                                                          = 54°

And m∠N = (5x + 27) = (5×9) + 27

                                   = 72°