Question

in the given figure lines AB and CD intersect at O. if angle BOC+angle BOE=70° and angle BOD=130°. find angle BOE and reflex angle AOC​

Answer 1

Step-by-step explanation:

1 . At first we have to know the angle of AOC

2 . Here,angle BOD=130°

Then for angle AOC=130°.

(vertically opposite angles)

3 . After that,angle BOC=50°

180°-130°=50°[supplementary angles]

4 . angle COB=50°

angle BOC+angle BOE=BOE=70°

5 . angle BOE=20°

(70° _ 50° =20°)

Therefore angle BOE=20°

6 . Reflex of angle AOC= 230°

(360° - 130° =230°)

Answer 2

Question :-

In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Answer :-

Since AB is a straight line,

∴ ∠AOC + ∠COE + ∠EOB = 180°

or (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)]

or ∠COE = 180° – 70° = 110°

∴ Reflex ∠COE = 360° – 110° = 250°

Also, AB and CD intersect at O.

∴∠COA = ∠BOD [Vertically opposite angles]

But ∠BOD = 40° [Given]

∴ ∠COA = 40°

Also, ∠AOC + ∠BOE = 70°

∴ 40° + ∠BOE = 70° or ∠BOE = 70° -40° = 30°

Thus, ∠BOE = 30° and reflex ∠COE = 250°.

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