Question

In Fig. 6.13, lines AB and CD intersect at O. IF
ZAOC + Z BOE = 70° and Z BOD = 40°. find
BOE and reflex 2 COE.​

Answer 1

Answer:

i) on line AB ,

angle AOC + angle BOE + angle COE= 180° (linear pair)

as we know the value of angle AOC + angle BOE = 70°

So, 70°+ angle COE= 180°

angle COE =180°-70° = 110°

Now let's find out the reflex angle COE =360°-110°=250°

ii) on line CD,

angle COE+ ANGLE BOE+ ANGLE BOD =180° (linear pair)

110°+ angle BOE + 40°=180°

150°+ angle BOE =180°

angle BOE= 180°-150°=30°

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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Hope it helps ❤