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?

Answer 1

108°

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°

Answer 2

x=108

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

`(x-36)\°+x\°=180\°\\2x=180+36\\2x=216\\x=108`