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

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

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 $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.

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

In the following figure,in $\Delta ABC$,$\angle ABC = 70^{\circ}$ and $\angle ACB = 60^{\circ}$. Find $\angle ABD$ and $\angle ACE$.

The measures of two vertically opposite angles are $(5x + 30^{\circ})$ and $(8x - 60^{\circ})$,then the value of $x = \dots$