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

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Rays OA, OB. OC, OD and OE have the common initial point O. Show that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.

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3. Prove “if two lines intersect each other, then the vertically opposite angles are equal.”

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4. In figure, OP bisects ∠AOC, OQ bisects ∠BOC and OP ⊥ OQ. Show that the points A, O and B are collinear.

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In figure, if y = 20°, prove that the line AOB is a straight line.

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∵ BOA is a line
(∠AOC + ∠BOE) + ∠EOC = 180°
⇒ 70° + EOC = 180°
⇒ ∠EOC = 110°
⇒ Reflex ∠EOC = 360° - 110° = 250°

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7. In figure, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

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8. In figure, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x, find ∠ROT.

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9. If the complement of an angle is one-third of its supplement, find the angle.

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10. In figure, find the value of x.

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