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,

AB

DB

=

EB

CB

or

10

5

=

8

CB

. It follows that CB=4, and so CE=CB+BE=4+8=12.