Two parallel lines l and m are cut by transversal t. For a pair of interior angles on one side of line t, the angle-bisectors are drawn to meet at point E. Find m .
A) 45°
B) 60°
C) 75°
D) 90°

Question

Two parallel lines l and m are cut by transversal t. For a pair of interior angles on one side of line t, the angle-bisectors are drawn to meet at point E. Find m  .
A) 45° 
B) 60° 
C) 75° 
D) 90°

Quizplus · Accepted Answer

When angle bisectors are drawn, the angle between them is the average of the two angles being bisected. Therefore, the two angles must have equal measures. Since they are on the same side of the transversal, they are supplementary, meaning their measures add up to 180 degrees. Therefore, each of the angles measures 90 degrees, and the angle between them, E, is also a right angle. So, m (the measure of angle E) is 90 degrees, corresponding to choice D.

Two Parallel Lines L and M Are Cut by Transversal