SAT Mathematics Practice Test 2

Angles ABE and DBC are vertical angles and thushave the same measure. Since segment AE is parallel to segment CD, anglesA and D are of the same measure by the alternate interior angle theorem.Thus, by the angle-angle theorem, triangle ABE is similar to triangle DBC,with vertices A, B, and E corresponding to vertices D, B, and C, respectively.Thus,$\frac{\mathit{A}\mathit{B}}{\mathit{D}\mathit{B}}=\frac{\mathit{E}\mathit{B}}{\mathit{C}\mathit{B}}$ or $\frac{10}{5}=\frac{8}{\mathit{C}\mathit{B}}$. It follows that $\mathit{C}\mathit{B}=4$, and so $\mathit{C}\mathit{E}=\mathit{C}\mathit{B}+\mathit{B}\mathit{E}=4+8=12$.