Find the angle between the bisectors of adjacent corners.

1. Let two adjacent angles ∠AOB = x and ∠COB = y be given. Since the sum of adjacent angles is 180 °, then:
x + y = 180 °.
Let us express y in terms of x:
y = 180 ° – x.
2. OM is the bisector ∠AOB. Since the bisector divides the angle in half, then:
∠AOM = ∠BOM = ∠AOB / 2 = x / 2.
ON is the bisector of ∠COB, then:
∠CON = ∠BON = ∠COB / 2 = y / 2 = (180 ° – x) / 2.
3. ∠MON – angle between OM and ON bisectors:
∠MON = ∠BOM + ∠BON = x / 2 + (180 ° – x) / 2 = (since two fractions have the same denominator, add their numerators) = (x + 180 ° – x) / 2 = 180 ° / 2 = 90 °.
Answer: the angle between the bisectors of adjacent angles is 90 °.