Question

In fig. 6.13 , lines AB and CD intersect at O. if angle AOC + angle BOE = 70° and angle BOD = 40° , find angle BOE and reflex angle COE​

Answer 1

Answer:

• ∠BOE = 30°
• Reflex ∠COE = 250°

Step-by-step explanation:

Given:

• ∠AOC + ∠BOE = 70°
• ∠BOD = 40°

To Find:

• ∠BOE
• Reflex ∠COE

By Linear pair,

⇒ ∠AOC + ∠BOE + ∠COE = 180°

⇒ 70° + ∠COE = 180°

⇒ ∠COE = 180° - 70°

⇒ ∠COE = 110°

Now, again by linear pair.

⇒ ∠COE + ∠BOE + ∠BOD = 180°

⇒ 110° + ∠BOE + 40° = 180°

⇒ 150° + ∠BOE = 180°

⇒ ∠BOE = 180° - 150°

⇒ ∠BOE = 30°

Hence, ∠BOE = 30°

Again by linear pair,

⇒ ∠AOD + ∠BOD = 180°

⇒ ∠AOD + 40° = 180°

⇒ ∠AOD = 180° - 40°

⇒ ∠AOD = 140°

Now, we will find reflex ∠COE

⇒ Reflex ∠COE = ∠AOC + ∠AOD + ∠BOD + ∠BOE

⇒ Reflex ∠COE = 40° + 140° + 40° + 30°

⇒ Reflex ∠COE = 250°

Hence, Reflex ∠COE = 250°