$\angle A$ and $\angle B$ are supplementary angles. If $\angle A : \angle B = 3 : 7$,then $\angle B = \dots$ (in $^o$)

Lines $AB$ and $CD$ intersect at $P$. If $\angle APC = 2x + 30^{\circ}$ and $\angle BPD = 4x - 20^{\circ}$,then find $x$,$\angle APC$,and $\angle BPD$.

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

How many triangles can be drawn having its angles as $53^{\circ}, 64^{\circ}$ and $63^{\circ}$? Give reason for your answer.

How many triangles can be drawn having its angles as $45^{\circ}, 64^{\circ}$ and $72^{\circ}$? Give reason for your answer.

In the figure,$x=y$ and $a=b$. Prove that $l \parallel n$.