How many triangles can be drawn having its angles as $45^{\circ}, 64^{\circ}$ and $72^{\circ}$? Give reason for your answer.

The difference between the supplementary angle and the complementary angle of any acute angle is............. (in $^{\circ}$)

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $I$. Prove that $\angle BIC = 90^{\circ} + \frac{1}{2} \angle A$.

$\angle X$ and $\angle Y$ are supplementary angles. If $\angle X : \angle Y = 23 : 13$,then find $\angle X$ and $\angle Y$.

An angle is $40^{\circ}$ less than its supplementary angle,then its measure is $\ldots \ldots \ldots .$ (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 $^{\circ}$)