Question

In the figure 1.89, seg AB $\parallel$ seg DC.Using the information given find sum of the the values of x.

Answer 1

In triangle OAB and OCD,
$\angle AOB=\angle COD$ (Vertically opposite angles)
$\angle BAO=\angle OCD$ (Alternate angles of parallel lines)
$\angle ABO=\angle ODC$ (Alternate angles of parallel lines)
Thus, $△OAB\sim △OCD$ (AAA rule)
Hence, $\frac{OD}{OB}=\frac{OC}{OA}$ (Ratio of corresponding sides of similar triangles is equal)
$\frac{3}{x-3}=\frac{x-5}{3x-19}$
$9x-57=(x-3)(x-5)$
$9x-57=x^2-8x+72$
$x^2-17x+72=0$
$x^2-11x-6x+72=0$
$(x-8)(x-9)=0$
$x=8,9$