Question

EXERCISE 6.1
In Fig. 6.13, lines AB and CD intersect at O. If
ZAOC + BOE = 70° and Z BOD= 40°, find
BOE and reflex 2 COE.​

Answer 1

Answer:

➢ Given :

Line AB and CD intersect at point O.

AOC +BOE = 70

BOD = 40

➢ To Prove :

BOE = ?

Reflex COE = ?

➢ Solution :

✬ AOC = BOD (Vertically Opposite angle)

✬ AOC = 40

AOC + BOE = 70(Given)

40 + BOE = 70

BOE = 70 - 40

BOE = 30

✬ AOC + COE + BOE = 180(Supplementary angle)

40 + COE + 30 = 180

COE + 70= 180

COE = 110

Reflex COE = 360- 110

COE = 250

Vertically opposite angles are the angles opposite each other when two lines cross.

The 2 angles are complementary, If there sum are 90

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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