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

Prove that a triangle must have at least two acute angles.

Ray $BD$ is the bisector of $\angle ABC$ and ray $BE$ is the bisector of $\angle DBC$. If $\angle EBC = 19^{\circ},$ then find $\angle DBC, \angle ABC$ and $\angle ABE$.

Prove that the sum of angles of any convex quadrilateral is $360^{\circ} .$

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

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