Question

In the given figure, lines AB and CD intersect at 0. if
AOC + BOE 70 and BOD = 40°, find BOE
and reflex COE.​

Answer 1

Answer:

Given:∠BOD=40 ∘

Since AB and CD intersects, ∠AOC=∠BOD(vertically opposite angles)

∠AOC=40 ∘

Also,∠AOC+∠BOE=70 ∘

⇒∠BOE=70 ∘

−∠AOC=70 ∘

−40 ∘

=30 ∘

We need to find reflex∠COE

Reflex∠COE=360 ∘

−∠COE

Now, ∠AOC+∠COE+∠BOE=180 ∘

⇒∠COE+(∠AOC+∠BOE)=180 ∘

⇒∠COE+(40 ∘

+30 ∘

)=180 ∘

⇒∠COE=180

∘

−70

∘

=110

∘

Reflex∠COE=360

∘

−110

∘

=250

∘

hope it will help......

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 :-

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°.