Q14 of 45 Page 164

Let and be two rays and let be a ray between and such that ∠AOX >∠XOB. Let OC be the bisector of ∠AOB.

∠AOX – ∠XOB = 2∠COX

13.JPG


⇒ ∠AOX - ∠XOB


⇒ (∠AOC + ∠COX) – (∠BOC - ∠COX)


⇒ ∠AOC - ∠BOC + 2∠COX


⇒ 2∠COX (∵ ∠AOC = ∠BOC)


More from this chapter

All 45 →
12

Let and be two lines intersecting at a point O. Let be a ray bisecting ∠BOD. Prove that the extension of to the left of O bisects ∠AOC.

 13

Let be a ray and let and be two rays on the same side of , with between and . Let be the bisector of ∠AOB. Prove that

∠XOA + ∠XOB = 2∠XOC

 15

Let be three rays such that lies between and . Suppose the bisectors of ∠AOC and ∠COB are perpendicular to each other. Prove that B, O, A are collinear.

 16

In the adjoining figure,

Prove that


∠ABC – ∠DCB + ∠CDE = 180°.