Question

If the bhi sectors of the adjacent angles are perpendicular to each other then prove that their outer arms are in the same straight line

Answer 1

see diagram.

Angles ABD and DBC are adjacent angles.BE and BF are their bisectors respectively.

Angle between bisectors :   EBF = x + y  = 90 deg.  (given)

So angle ABC = angle ABD + angle DBC
                      = 2x+2y = 2 (x+y) = 2 * 90 = 180 deg.

So that means that the outer arms AB  and BC of the two adjacent angles are along the same line.

Answer 2

Answer:

The above answer is correct and could be reffered to.

Hope this comment helped you.