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Problem of the Week
Problem E
Find Another Angle

The points \(A\), \(B\), \(D\), and \(E\) lie on the circumference of a circle with centre \(C\), as shown.

Points A, B, D, and E are placed, in order, around the circle with A and D on opposite sides of the circle and sector BCD with an angle of 72 degrees. Line segments AB, BC, CD, DE, and EA form a five-sided figure inside the circle.

If \(\angle BCD=72\degree\) and \(CD=DE\), then determine the measure of \(\angle BAE\).