Question

In the below fig, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF,
∠DOE and ∠BOF.

Answer 1

`∠`AOE and `∠`EOB are linear pair of angles

`∠`AOE + `∠`EOB = 180°

`∠`AOE + `∠`DOE + `∠`BOD = 180°

⇒ `∠`DOE = 180° - 40° - 35° = 105°

Vertically opposite side angles are equal

`∠`DOE = `∠`COF = 105°

Now, `∠`AOE + `∠`AOF = 180°                [∵ Linear pair]

⇒  `∠`AOE + `∠`AOC + `∠`COF = 180°

⇒ 40° + `∠`AOC +105° = 180°

⇒ `∠`AOC = 180° -145°

⇒ `∠`AOC = 35°

Also, `∠`BOF = `∠`AOE = 40°                    [  ∵ Vertically opposite angle are equal]