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Angle Bisector

Ray OE bisect...

Question

Ray OE bisects $∠$ AOB and OF is the ray opposite OE, then $∠$ FOB $=$ __________.

∠

FOA

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∠

BOE

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∠

AOE

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None of these

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Solution

The correct option is A $∠$ FOA
$O E$ is the angle bisector as shown in the figure, then
$∠ 1 = ∠ 2$
and $O F$ is the ray opposite to $O E$ , then
$∠ 1 + ∠ 3 = ∠ 2 + ∠ 4 = 180^{o} \Rightarrow ∠ 3 = ∠ 4 \Rightarrow ∠ F O B = ∠ F O A$

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Similar questions

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and

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In the figure, rays OA, OB, OC, OD and OE have the common end point O. Show that $∠ A O B + ∠ B O C + ∠ C O D + ∠ D O E + ∠ E O A = 360^{\circ}$ .

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Prove that:

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[

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Ray OE bisects ∠AOB and OF is the ray opposite OE, then ∠FOB= __________.

The correct option is A ∠FOAOE is the angle bisector as shown in the figure, then ∠1=∠2and OF is the ray opposite to OE, then∠1+∠3=∠2+∠4=180o⇒∠3=∠4⇒∠FOB=∠FOA

Ray OE bisects $∠$ AOB and OF is the ray opposite OE, then $∠$ FOB $=$ __________.

The correct option is A $∠$ FOA
$O E$ is the angle bisector as shown in the figure, then
$∠ 1 = ∠ 2$
and $O F$ is the ray opposite to $O E$ , then
$∠ 1 + ∠ 3 = ∠ 2 + ∠ 4 = 180^{o} \Rightarrow ∠ 3 = ∠ 4 \Rightarrow ∠ F O B = ∠ F O A$