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

Ray $YM$ is the bisector of $\angle XYZ$ and ray $YN$ is the bisector of $\angle MYZ$. If $\angle XYN = 45^{\circ}$,then find $\angle XYZ$. (in $^{\circ}$)

$\angle P$ and $\angle Q$ are complementary angles. If $\angle P = 3x + 15^{\circ}$ and $\angle Q = x + 7^{\circ}$,then find $\angle P$ and $\angle Q$.

In the figure,the sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ respectively. If the bisectors $BO$ and $CO$ of $\angle CBE$ and $\angle BCD$ respectively meet at point $O$,then prove that $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.

In the following figure,$\angle DBC = 70^{\circ}$ and ray $BP$ is the bisector of $\angle DBA$. Find $\angle PBC$ and reflex $\angle PBD$.

$\angle X$ and $\angle Y$ are supplementary angles. If $\angle X : \angle Y = 23 : 13$,then find $\angle X$ and $\angle Y$.