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?

x=108

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

m∠RQS≅m∠QLK -----> by corresponding angles

m∠KLM+m∠QLK=180° -----> by supplementary angles (consecutive interior angles)

we have that

m∠RQS=x° ----> given problem

so

m∠QLX=x°

m∠KLM=(x-36)° ----> given problem

substitute

108°

Step-by-step explanation:

Angle RQS is congruent to angle QLK. Angle RQS is x degrees, then angle  QLK is x degrees

.

Line RM intersects line KN at point L, then angle KLM, which is (x minus 36) degrees, is complementary to angle QLK. In consequence:

x - 36° + x = 180°

2*x = 180° +36°

x = 216°/2

x = 108°