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?
2 answers:
Answer:
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
![(x-36)\°+x\°=180\°\\2x=180+36\\2x=216\\x=108](https://tex.z-dn.net/?f=%28x-36%29%5C%C2%B0%2Bx%5C%C2%B0%3D180%5C%C2%B0%5C%5C2x%3D180%2B36%5C%5C2x%3D216%5C%5Cx%3D108)
Answer:
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°
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