In $\Delta XYZ$,$\angle X : \angle Y : \angle Z = 1 : 4 : 4$,then $\angle Z = \ldots$ (in $^{\circ}$)

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $I$. Prove that $\angle BIC = 90^{\circ} + \frac{1}{2} \angle A$.

$\angle A = \angle B$. If $\angle A$ and $\angle B$ are supplementary angles,then $\angle A = \ldots$ (in $^o$)

In the given figure,find the values of $x$ and $y$ and then show that $PQ \parallel XY.$

Find the measure of an angle,which is one-eighth of the measure of its supplementary angle. (in $^o$)

$A$ triangle $ABC$ is right-angled at $A$. $L$ is a point on $BC$ such that $AL \perp BC$. Prove that $\angle BAL = \angle ACB$.