In the given figure,if $AB \parallel CD$,$\angle PCD = 130^{\circ}$ and $\angle PBA = 140^{\circ}$,then find $\angle BPC$. (in $^{\circ}$)

$\angle ABD$ and $\angle DBC$ are adjacent angles. If $\angle ABD = 1.5x^{\circ}$,$\angle DBC = 2x^{\circ}$,and $\angle ABC = 70^{\circ}$,then find $x$ and the measures of $\angle ABD$ and $\angle DBC$.

The complementary angle of the supplementary angle of an angle having measure $132^{\circ}$ has measure $\ldots \ldots \ldots .$. (in $^{\circ}$)

In $\Delta ABC$,the sides $AB$ and $AC$ are produced to $D$ and $E$ respectively,so that exterior angles $\angle CBD$ and $\angle BCE$ are formed. If bisectors of $\angle CBD$ and $\angle BCE$ intersect at point $O$,prove that $\angle BOC = 90^{\circ} - \frac{1}{2} \angle A$.

$\angle P$ and $\angle Q$ are supplementary angles. If $\angle P = 11 \angle Q$,then find $\angle P$ and $\angle Q$.

$\angle A$ and $\angle B$ are complementary angles. If $\angle A = \angle B - 20^{\circ}$,then find $\angle A$ and $\angle B$.