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Lines and Angles
Question
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Ray OE bisects ∠AOB and OF is the ray opposite to OE. Show that ∠FOB = ∠FOA.

Answer

∠FOB + ∠BOE = 180° ...(1)
| Linear Pair Axiom
∠FOA + ∠AOE = 180° ...(2)
| Linear Pair Axiom
From (1) and (2),
∠FOB + ∠BOE = ∠FOA + ∠AOE ...(3)
But    ∠BOE = ∠AOE
| ∵ Ray OE bisects ∠AOB
∴ From (3),
⇒    ∠FOB = ∠FOA.

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