2024 InIMC keystage2-EMIC team Question 6

In the diagram below, triangle $ABC$ is a right triangle at $A$ with $AC>AB$. Let point $M$ be on ray $BA$ such that $BM=AC$. Let point $N$ be outside triangle $ABC$ and on the ray $AC$ such that $CN=AM$. If ray $MC$ intersects $BN$ at $P$, what is the measure, in degrees, of $\angle MPB$?





Paper instruction: Give a full solution.