In the given figure lines \(\overline {AB}\, and \,\overline {CD}\)

1.	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» 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°

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»

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°