Question

If quadrilateral LMNO is a parallelogram, what must the measure of angle LMN be?

Answer 1

105 got it right on edg.

Answer 2

Answer:

∠LMN = 105°

Step-by-step explanation:

Quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°

We have get the measurement of ∠LMN

Since in a parallelogram opposite angles are equal.

Therefore 25x = 22x + 9

25x - 22x = 9

3x = 9

x = 3

From another property of a parallelogram we know that consecutive angles are supplementary.

∠LMN + ∠ONM = 180°

∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)

∠LMN = 180 - 75 = 105°

Answer is ∠LMN = 105°