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

Angles of a triangle are in the ratio $2: 4: 3$. The smallest angle of the triangle is (in $^{\circ}$)

In $\Delta ABC$,if $\angle A = \angle B + \angle C$,then $\angle A = \ldots$ (in $^{\circ}$)

Bisectors of angles $B$ and $C$ of a triangle $ABC$ intersect each other at the point $O$. Prove that $\angle BOC = 90^{\circ} + \frac{1}{2} \angle A$.

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

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.