In the diagram, P is on RS so that QP bisects < SQR. Also, PQ=PR, < RSQ=2y degrees, and < RPQ=4y degrees. What is the measure, in degrees, of < RPQ?
Note that if PQ =PR, then angles PRQ and PQR = x
So.....we have this system
2y + 3x = 180 (1)
4y + 2x = 180 ⇒ 2x = 180 - 4y ⇒ x = 90 - 2y (2)
Sub (2) into (1) for x
2y + 3 ( 90 - 2y) = 180
2y + 270 - 6y = 180
-4y = 180 - 270
4y = 270 - 180 = 90° = angle RPQ
