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

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2:3,$ then the greater of the two angles is (in $^{\circ}$)

In the given figure,find the value of $x$ for which the lines $l$ and $m$ are parallel.

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

Two lines $l$ and $m$ are perpendicular to the same line $n$. Are $l$ and $m$ perpendicular to each other? Give reason for your answer.

In $\Delta ABC$,$\angle B = \frac{\angle A + \angle C}{2}$ and $\angle A : \angle C = 1 : 2$. Find the measure of each angle of $\Delta ABC$.