Problem 174

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Problem 174: (2011 AMC 10b, 17)

In the given circle, the diameter $\overline{EB}$ is parallel to $\overline{DC}$, and $\overline{AB}$ is parallel to $\overline{ED}$. The angles $AEB$ and $ABE$ are in the ratio $4 : 5$. What is the degree measure of angle $BCD$?

$\textbf{(A)}\ 120 \qquad$ $\textbf{(B)}\ 125 \qquad$ $\textbf{(C)}\ 130 \qquad$ $\textbf{(D)}\ 135 \qquad$ $\textbf{(E)}\ 140$

Solution

Exercise 174: Solution

In a circle, the diameter $\overline{EB}$ is parallel to the chord $\overline{DC}$, and the chord $\overline{AB}$ is parallel to the chord $\overline{ED}$. The angles $AEB$ and $ABE$ are in the ratio $2:7$. What is the degree measure of angle $BCD$?

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