Find the measure of the supplementary angle of an angle of $52^{\circ}$. (in $^{\circ}$)

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

The angles of a triangle are in the ratio $2: 3: 4$. Find the angles of the triangle.

If the measure of an acute angle is $x^{\circ}$,find the difference of the measure of its supplementary angle and complementary angle. (in $^{\circ}$)

In $\Delta ABC$,$\angle A = 2x - 10^{\circ}$,$\angle B = x + 10^{\circ}$,and $\angle C = 2x - 20^{\circ}$. Find the measure of each angle of $\Delta ABC$.

$AP$ and $BQ$ are the bisectors of the two alternate interior angles formed by the intersection of a transversal $t$ with parallel lines $l$ and $m$ (see figure). Show that $AP \parallel BQ$.