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

In the given figure,in $\Delta PQR$,$\angle Q > \angle R$. $PM \perp QR$ and $PA$ is the bisector of $\angle QPR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.

In $\Delta ABC$,$\angle B = 70^{\circ}$ and $\angle C = 80^{\circ}$. The bisector of $\angle A$ intersects $BC$ at $D$. Find $\angle ADB$ and $\angle ADC$.

Let $OA, OB, OC$ and $OD$ be rays in the anticlockwise direction such that $\angle AOB = 100^{\circ}, \angle COD = 100^{\circ}, \angle BOC = 82^{\circ}$ and $\angle AOD = 78^{\circ}$. Is it true to say that $AOC$ and $BOD$ are lines?

$\angle ACD$ is an exterior angle of $\Delta ABC$. The bisector of $\angle ABC$ and exterior $\angle ACD$ intersect each other at point $E$. Prove that,$\angle BEC = \frac{1}{2} \angle BAC$.

State whether each of the following statements is true or false:
$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.
$(2)$ The maximum number of acute angles in any triangle is two.