Prove that the bisectors of two adjacent supplementary angles include a right angle.
Secondary school Mathematics for class 9
Given, ∠AOC and ∠BOC are supplementary angles
OE is the bisector of ∠BOC and
OD is the bisector of ∠AOC
Therefore, ∠1 = ∠2 and ∠3 = ∠ 4 ________________ (i)
∠BOC + ∠AOC = 180° [Because AOB is a straight line]
⇒ ∠1 + ∠2 + ∠3 + ∠4 = 180°
⇒ ∠1 + ∠1 + ∠3 + ∠3 = 180° [From equation (i)]
⇒ 2 ∠1 +2 ∠3 = 180°
⇒ 2(∠1 + ∠3) = 180°
⇒ ∠1 + ∠3 = 90°
Hence, ∠EOD = 90° proved.