Problem 265

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Problem 265: (2009 AMC 12b, 16)

Trapezoid $ABCD$ has $AD||BC$, $BD = 1$, $\angle DBA = 23^{\circ}$, and $\angle BDC = 46^{\circ}$. The ratio $BC: AD$ is $9: 5$. What is $CD$? $\textbf{(A)}\ \frac {7}{9}\qquad$ $ \textbf{(B)}\ \frac {4}{5}\qquad$ $ \textbf{(C)}\ \frac {13}{15} \qquad$ $ \textbf{(D)}\ \frac {8}{9}\qquad$ $ \textbf{(E)}\ \frac {14}{15}$

Solution

Exercise 265: Solution

Trapezoid $ABCD$ has $AD||BC$, $BD = 1$, $\angle DBA = 25^{\circ}$, and $\angle BDC = 50^{\circ}$. The ratio $BC: AD$ is $2: 1$. What is $CD$?

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