Find the measure of the complementary angle of the supplementary angle of an angle having measure $128^{\circ}$. (in $^{\circ}$)

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

The supplementary angle of the complementary angle of an angle having measure $32^{\circ}$ has measure.......... (in $^{\circ}$)

If one of the two angles of a linear pair has measure $x^{\circ},$ then the other angle has measure of $\ldots \ldots . .$

$\angle ACD$ is an exterior angle of $\Delta ABC$. The bisector of $\angle ABC$ and exterior $\angle ACD$ intersect each other at point $E$. Prove that,$\angle BEC = \frac{1}{2} \angle BAC$.

$\angle A$ and $\angle B$ are complementary angles. If $\angle A : \angle B = 1 : 5$,then find $\angle A$ and $\angle B$.