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?
Accepted Solution
A:
Answer:x=108Step-by-step explanation:see the attached figure to better understand the problemwe know thatm∠RQS≅m∠QLK -----> by corresponding angles m∠KLM+m∠QLK=180° -----> by supplementary angles (consecutive interior angles)we have thatm∠RQS=x° ----> given problemsom∠QLX=x°m∠KLM=(x-36)° ----> given problemsubstitute[tex](x-36)\°+x\°=180\°\\2x=180+36\\2x=216\\x=108[/tex]