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Lines and Angles

Short Answer Type

11. In figure, if ∠POR and ∠QOR form a linear pair and a - b = 80° then find the value of a and b.

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12. What value of x would make XOY a line if ∠XOZ = 7x + 20° and ∠YOZ = 3x in figure.

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13. An angle is

open parentheses 1 fifth close parentheses to the power of t h end exponent

of its supplement. Find the angle.

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14. Two supplementary angles are in the ratio 4 : 5. Find the angles.

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15. In figure, lines AB and CD intersect at O. If ∠AOD : ∠DOC = 4 : 5 then find ∠COB.

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16.

An angle is equal to five times of its complement. Find the measure of the angle.

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17. In figure, lines I and m intersect each other at O. If x = 40°, then, find the values of y, z and w.

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18. If OA, OB. OC and OD are the rays such that ∠AOB = ∠COD = 150°, ∠BOC = 30° and ∠AOD = 30°. Is it true that AOC and BOD are straight lines? Justify your answer.

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19. In figure, angles x and y are supplementary angles. If ∠x = 110°, find the value of y.

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20. In figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

∵ Lines AB and CD intersect at O
∴ ∠AOC = ∠BOD
| Vertically Opposite Angles
But ∠BOD = 40° ...(1) | Given
∴ ∠AOC = 40° ...(2)
Now, ∠AOC + ∠BOE = 70°
⇒ 40° + ∠BOE = 70° | Using (2)
⇒ ∠BOE = 70° - 40°
⇒ ∠BOE = 30°
Again,
Reflex ∠COE
= ∠COD + ∠BOD + ∠BOE
= ∠COD + 40° + 30°
| Using (1) and (2)
= 180° + 40° + 30°
| ∵ Ray OA stands on line CD
|∴ ∠AOC + ∠AOD = 180° (Linear Pair Axiom) ⇒ ∠COD = 180°
= 250°.

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