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IMAS 2023–2024 Junior Division — Round 2 Question 7

IMAS · IMAS 2023–2024 Junior Division — Round 2

Question 7

In triangle $ABC$, $\angle BAC=30^\circ$ and $\angle ABC=105^\circ$. Let $P$ be a point inside the triangle such that $\angle PAB=15^\circ$ and $\angle ABP=75^\circ$, as shown in the diagram below. What is the measure, in degrees, of $\angle PCB$?

Question illustration