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

Question

In the given figure lines \(\overline {AB}\, and \,\overline {CD}\) intersect at ’O’. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Answer 1

Given that ∠AOC +∠BOE = 70° 

∠BOD = 40° 

∠AOC = 40° 

(∵ ∠AOC, ∠BOD are vertically opposite angles) 

∴ 40° + ∠BOE = 70° 

⇒ ∠BOE = 70° – 40° = 30° 

Also ∠AOC + ∠COE +∠BOE = 180°

( ∵ AB is a line) 

⇒ 40° + ∠COE + 30° = 180° 

⇒ ∠COE = 180° -70° = 110° 

∴ Reflex ∠COE = 110°