In the diagram, $P$ is on $RS$ so that $QP$ bisects $\angle SQR$. Also, $PQ=PR$, $\angle RSQ=2y^\circ$, and $\angle RPQ=3y^\circ$. What is the measure, in degrees, of $\angle RPQ$?
By the exteriror angle theorem, 3y = 2y + x ⇒ 3y - 2y = x ⇒ y = x
And in triangle PQR, since PQ = RQ, then angle PQR = angle PRQ = x
So
3y + x + x = 180
And since y = x
3x + x + x = 180
5x = 180
x = 36
So 3x = 3y = 3(36) = 108°
