Question

The bisectors of opposite angles are parallel to each other.

Answer 1

$ABCD$ is aparallelogram.

$AP$ bisects $\angle A$ and $CQ$ bisects $\angle C$.

Opposite angles of a parallelogram are equal. SO, $\angle A=\angle C$ and $\angle B=\angle D$

So, $\angle DAP=\angle BCQ$, $AD=BC$, $\angle B=\angle D$

$\therefore$ By $ASA$ congruency, $AP=QC$.

$\therefore$ $APCQ$ is parallelogram and $AP\parallel CQ$.