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

In a triangle $ABC$,$D$ is the mid-point of side $AC$ such that $BD = \frac{1}{2} AC$. Show that $\angle ABC$ is a right angle.

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

$P$ is a point on the bisector of $\angle ABC$. If the line through $P$,parallel to $BA$,meets $BC$ at $Q$,prove that $\triangle BPQ$ is an isosceles triangle.

Prove that the sum of the three angles of a triangle is $180^{\circ}$.

$ABC$ is a triangle. Locate a point in the interior of $\Delta ABC$ which is equidistant from all the vertices of $\Delta ABC$.