MathNet 2024-part-01 — 168 problems (EN–VI) Question 66

Given is a triangle $ABC$ and the points $M$, $P$ lie on the segments $AB$, $BC$, respectively, such that $AM = BC$ and $CP = BM$. If $AP$ and $CM$ meet at $O$ and $2\angle AOM = \angle ABC$, find the measure of $\angle ABC$.