Question

Look at the diagram in the image attached.

What is the measure of LLMN?
A. 67°
B. 71°
C. 109°
D. 113°

Answer 1

67°

Explanation:

Sum of the interior angles of a triangle = 180

To find x, set the sum of the supplementary angles to the 3 shown angles (x-6, x+9, x) equal to 180:

180 = (180-x+6) + (180-x-9) + (180-x)

180 = 536 - 3x

-357 = -3x

x = 119

119 - 6 = 113 this is the angle supplementary to ∠LMN, therefore:

m∠LMN = 180 - 113 = 67°