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°