Question

i will be greatefull,if you help me in answering the below problem:

1.)Prove that the bisectors of two adjacent supplementary angles include a right angle.

Answer 1

Let the supplementary angles be
A and B . You can call them also A and 180-A, since they are supplementary.

Draw a straight line and let a second line join it at point O, to divide the straight line into a zero degree line and a 180 degree line. The space above the line is divided into angles A and 180 - A.

The bisector of A is A/2 degrees from the zero degree line.
The bisector of B is A + (180-A)/2 from the zero degree line.

The angle between the two bisectors is
A + (180-A)/2 -A/2 = 90

Answer 2

Prove that the bisector of two adjacent supplementary angle include a right angle