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MathNet 2013 Question 19

Math Olympiad Vault · MathNet 2013

Question 19

Júlio Daniel has a square sheet of paper with vertices $A,B,C,D$. He first folds it by bringing vertices $B,D$ to the diagonal as shown:
Question illustration
He then brings vertex $C$ to $A$, obtaining a pentagon as shown:
Question illustration
a) Prove that angle $a$ measures $90^\circ$.
b) Determine angle $b$.