In the figure above, AE || CD and segment AD intersects segment CE at B. What is the length of segment CE ?

Explanation

The correct answer is 12. Angles ABE and DBC are vertical angles and thus have the same measure. Since segment AE is parallel to segment CD, angles A 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, `(AB)/(DB)=(EB)/(CB) or (10)/(5)=(8)/(CB)` . It follows that CB = 4, and so `CE = CB + BE = 4 + 8 =12.`