Question

What is the value of x?

Answer 1

Answer:

$x = 25$

Solution:

$\frac{40}{40+24} = \frac{x}{x +15} \\ \frac{40}{64} = \frac{x}{x +15} \\ \frac{5}{8} = \frac{x}{x +15} \\ 5(x +15) = 8x \\ 5x +75 = 8x \\ 75 = 3x \\ 25 = x$

Explanation:

Angle BDR is congruent to angle QDC because they share common angles. Angles BRD and QCD are congruent because lines BR and QC are parallel and line DR intersecting them creates two corresponding angles, BRD and QCD. Because of the reasons I mentioned, Triangles DBR and DQC are similar by Angle Angle Similarity Postulate and because these two triangles are similar they must share the same scaling factor of corresponding sides (example: $\frac{DQ}{DB}$). So $\frac{DQ}{DB} = \frac{DC}{DR}$.