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Let  B, A, and D be three consecutive vertices of a regular 20-gon. A regular heptagon is constructed on line AB with a vertex C next to A. Find angle BCD in degrees.

 May 12, 2023
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Let O be the center of the regular 20-gon. Since ∠OBA=180∘−360∘/20​=135∘, we have ∠OCA=1/2​⋅135∘=67.5∘. Since ∠OAC=∠OBC=120∘, we have ∠BCD=180∘−∠OCA−∠OAC−∠OBC=72.5∘​.

 May 12, 2023

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