Find the measure of the supplementary angle of the complementary angle of an angle having measure $62^{\circ}$. (in $^{\circ}$)

$AP$ 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 $AP \parallel BQ$.

Find the measure of the complementary angle of an angle of $44^{\circ}$. (in $^{\circ}$)

For what value of $x+y$ in the figure will $ABC$ be a straight line? Justify your answer.

$\angle X$ and $\angle Y$ are complementary angles. If $\angle X = 4 \angle Y$,then find $\angle X$ and $\angle Y$.

An angle whose measure is $90^{\circ}$ is called a $\ldots \ldots \ldots$