Question

In the figure, AngleRQS Is-congruent-to AngleQLK.

3 lines are shown. Lines S P and K N are parallel. Line R M intersects line S P at point Q, and intersects line K N at point L. Angle R Q S is x degrees. Angle K L M is (x minus 36) degrees.
What is the value of x?

36
72
108
144

Answer 1

Angle RQS = angle QLK = x (given). Points Q, L, M are collinear (RM is the transversal), so angles QLK and KLM form a linear pair and are supplementary:
x + (x − 36) = 180
2x − 36 = 180
2x = 216
x = 108.

Answer: 108.