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.
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∘.