SATMathematics Practice Test 1

It is given that ∠AEB and ∠CDB have the same measure. Since ∠ABE and ∠CBD are vertical angles, they have the same measure.
Therefore, triangle EAB is similar to triangle DCB because the triangles have two pairs of congruent corresponding angles (angle angle criterion for similarity of triangles).
Since the triangles are similar, the corresponding sides are in the same proportion; thus $\frac{\mathit{C}\mathit{D}}{\mathit{x}}=\frac{\mathit{B}\mathit{D}}{\mathit{E}\mathit{B}}$
Substituting the given values of 800 for CD 700 for BD, and 1400 for EB in $\frac{\mathit{C}\mathit{D}}{\mathit{x}}=\frac{\mathit{B}\mathit{D}}{\mathit{E}}\mathit{B}$ gives $\frac{800}{\mathit{x}}=\frac{700}{1400},$
Therefore, $\mathit{x}=\frac{\left(800\right)\left(1400\right)}{700}=1600$