Question

If two parallel lines are intersected by a transversal then prove that bisectors of one pair of interior angles intersect at right angles.

Answer 1

after you draw the diagram... you would get co interior angles.
and sum of them is 180°
when you bisect the angles such that the bisectors meet at a point.
thus the angles' sum would be 180/2=90
since we get a triangle then the 3rd angle would become
180-90=90
proved
hope it helped

Answer 2

Solutions:

We know that the sum of interior angles on the same side of the transversal is 180°.

Hence, ∠BMN + ∠DNM = 180°

=> 1/2∠BMN + 1/2∠DNM = 90°

=> ∠PMN + ∠PNM = 90°

=> ∠1 + ∠2 = 90° ............. (i)

In △PMN, we have

∠1 + ∠2 + ∠3 = 180° ......... (ii)

From (i) and (ii), we have

90° + ∠3 = 180°

=> ∠3 = 90°

=> PM and PN intersect at right angles.