If two lines intersect each other,then the vertically opposite angles are.........

In the figure,$\angle Q > \angle R$,$PA$ is the bisector of $\angle QPR$ and $PM \perp QR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.

In $\Delta ABC$,$\angle B = 70^{\circ}$ and $\angle C = 80^{\circ}$. The bisector of $\angle A$ intersects $BC$ at $D$. Find $\angle ADB$ and $\angle ADC$.

If two parallel lines are intersected by a transversal,then interior angles on the same side of the transversal are $\ldots \ldots . . .$

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

In the figure,if $AB \parallel CD$,$\angle BMX = 125^{\circ}$ and $\angle CNX = 55^{\circ}$,find $\angle MXN$. (in $^{\circ}$)