Question

In the given figure AB, CD and EF are the three concurrent lines at O. Then find the value of angle AOC+ angle BOE​

Answer 1

Answer:

Given ∠AOE = 40° & ∠BOD = 35°

Clearly ∠AOC = ∠BOD [Vertically opposite angles]

⇒ ∠AOC = 35° Ans.

∠BOF = ∠AOE [Vertically opposite angles]

⇒ ∠BOF = 400 Ans.

Now, ∠AOB = 180° [Straight angles]

⇒ ∠AOC + ∠COF + ∠BOF = 180° [Angles sum property] ⇒ 35° + ∠COF + 40° = 180°

⇒ ∠COF = 180° - 75° = 105°

Now, ∠DOE = ∠COF [Vertically opposite angles]

∴ ∠DOE = 105°