Question

What is y in terms of x

Answer 1

9514 1404 393

Answer:

  E.  4x -180

Step-by-step explanation:

Angles QPB and RAP are corresponding, so congruent. Angles QPR and ARP are alternate interior angles, so congruent. Triangles BQP and PQR are isosceles, so angle PBQ ≅ angle QPB and angle RQP = 180-2x.

The total of angles RQP and RQC is angle PQC, an external angle to triangle PQB. We know the exterior angle is equal to the sum of the remote interior angles. That  means ...

  angle PQC = angle QPB +angle QBP

  y +(180 -2x) = x + x

  y = 4x -180 . . . . . . . . . . . subtract (180-2x) from both sides