The sum of a linear pair of angles is always.......... (in $^{\circ}$)

An exterior angle of a triangle is $105^{\circ}$ and its two interior opposite angles are equal. Each of these equal angles is

$A$ transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

How many triangles can be drawn having its angles as $53^{\circ}, 64^{\circ}$ and $63^{\circ}$? Give reason for your answer.

In the figure,$BA \parallel ED$ and $BC \parallel EF.$ Show that $\angle ABC + \angle DEF = 180^{\circ}.$

$\angle P$ and $\angle Q$ are complementary angles. If $\angle P = 3x + 15^{\circ}$ and $\angle Q = x + 7^{\circ}$,then find $\angle P$ and $\angle Q$.