Question

The bisectors of two adjacent supplementary angels are always at ________.

Answer 1

OP is the bisector of ∠BOC.

∴ ∠BOP = ∠COP = $\frac{\angle \mathrm{BOC}}{2}$ .....(1)

OQ is the bisector of ∠AOC

∴ ∠AOQ = ∠COQ = $\frac{\angle \mathrm{AOC}}{2}$ .....(2)

It is given that,

∠AOC and ∠BOC are two adjacent supplementary angles.

∴ ∠BOC + ∠AOC = 180º

⇒ 2∠POC + 2∠COQ = 180º

⇒ ∠POC + ∠COQ = $\frac{180°}{2}$ = 90º

⇒ ∠POQ = 90º

Thus, the bisectors of two adjacent supplementary angles are always at right angle i.e. 90º.

The bisectors of two adjacent supplementary angels are always at __right angle__.