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