Question

In the figure, examine whether lines $AB$ and $CD$ are parallel or not:

Answer 1

Step: Examine whether the lines are parallel

Linear pairs are supplementary
$\Rightarrow \angle APF+\angle BPF={180}^{\circ }$
$\Rightarrow \angle APF+{115}^{\circ }={180}^{\circ }$
$\Rightarrow \angle APF={180}^{\circ }-{115}^{\circ }={65}^{\circ }$

If two parallel lines are intersected by a transversal, each pair of corresponding angles is equal.

$\Rightarrow \angle APF=\angle CQF$ (Corresponding angles)
$\Rightarrow {65}^{\circ }={65}^{\circ }$
$\therefore AB\parallel CD$