Question

At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?

Answer 1

Same-side interior angles are a pair of angles on one side of a transversal line, and on the inside of the two parallel lines being intersected.

The sum of same-side interior angles is equal to 180 degrees.

A transversal line is a line that intersects other lines.

Parallel lines are lines that run alongside each other that never intersect.

An angle bisector is a line that divides an angle into two equal parts.

Given that the sum of same side interior angles is equal to 180 degrees, then the sum of the angle formed by the angle bisector is equal to 90 degrees.
Thus the angle bisectors intersect at an angle 90 degrees.

Therefore, the angle bisectors of two same side interior angles in construction with two parallel lines and a transversal intersect at angle 90 degrees.