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Again, someone thats not a guest explain this question please.

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Let B, A, and D be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on $$\overline{AB}$$, with a vertex C next to A. Find $$\angle BCD$$, in degrees.

May 15, 2020

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Let B, A, and D be three consecutive vertices of a regular 18-gon.
A regular heptagon is constructed on $$\overline{AB}$$, with a vertex C next to A.
Find $$\angle BCD$$, in degrees.

The inscribed $$\angle BCD$$ is half of the central $$\angle BAD$$

$$\begin{array}{|rcll|} \hline \angle BCD &=& \dfrac{\angle BAD}{2} \\ && \boxed{\angle BAD = \dfrac{16*180^\circ}{18}\\ \angle BAD =160^\circ } \\ \angle BCD &=& \dfrac{160^\circ}{2} \\ \mathbf{\angle BCD} &=& \mathbf{80^\circ } \\ \hline \end{array}$$

May 15, 2020