Zig, say hello to Zag .....

Geometry Level 5

Inside a square \(ABCD\) points \(P\) and \(Q\) are positioned so that \(DP || QB\) and \(DP = PQ = QB\). Of all configurations that satisfy these requirements, what is the minimum possible value of \(\angle ADP\), (in degrees)?

(This is not an original, but I nevertheless thought it was worth sharing.)

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