$\angle A = \angle B$. If $\angle A$ and $\angle B$ are supplementary angles,then $\angle A = \ldots$ (in $^o$)

Prove that through a given point,we can draw only one perpendicular to a given line.

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

In the given figure,in $\Delta PQR$,$\angle Q > \angle R$. $PM \perp QR$ and $PA$ is the bisector of $\angle QPR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

Bisectors of angles $B$ and $C$ of a triangle $ABC$ intersect each other at the point $O$. Prove that $\angle BOC = 90^{\circ} + \frac{1}{2} \angle A$.