Prove that the angle between the bisectors of adjacent angles is 90 degrees.

Adjacent angles are the angles formed when two lines intersect. The sum of two adjacent angles is 180 degrees.
At the intersection of straight lines AB and OC at point O, two adjacent angles were formed. AOC angle and COB angle. The bisector OK of the AOC angle and the bisector OM of the COB angle divided these angles in half and the angle between the bisectors is equal to the sum of these angles. The sum of the AOC angle and the COB angle is 180 degrees, that is, the angle formed by the bisectors is 180/2 = 90 degrees.