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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 \(\angle BAD\)

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

 

laugh

 May 15, 2020

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