In the diagram below, we have ¯AB∥¯CD,QP=QR ,∠BPQ=x∘+100∘ , and ∠APR=x∘. Find x.
https://latex.artofproblemsolving.com/2/3/6/23637a6b4f6218e50583ee5b39bcc517771d75a8.png
x = 144/5
Angle APR==Angle PRQ ==x
Angle PRQ ==Angle QPR==x {Because triangle PQR is an isosceles triangle}
Angle BPQ ==Angle PQR ==100 + x
From isosceles triangle PQR, we have:
(100 + x) + x + x ==180
3x ==180 - 100 ==80
x ==80 / 3 ==26 + 2/3 == 26.6667 degrees
+24 
