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

Ray $YM$ is the bisector of $\angle XYZ$ and ray $YN$ is the bisector of $\angle MYZ$. If $\angle XYN = 45^{\circ}$,then find $\angle XYZ$. (in $^{\circ}$)

In the given figure,$AB \parallel DE$ and $BC \parallel EF$. Prove that $\angle ABC + \angle DEF = 180^{\circ}$.

Bisectors of interior $\angle B$ and exterior $\angle ACD$ of a $\triangle ABC$ intersect at the point $T$. Prove that $\angle BTC = \frac{1}{2} \angle BAC.$

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

$\angle ACD$ is an exterior angle of $\Delta ABC$ and the bisector of $\angle A$ intersects $BC$ at $E$. Prove that $\angle ABC + \angle ACD = 2 \angle AEC$.