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

∠DOE and ∠BOF.

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#### 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

*`∠`DO**E *= `∠`*C**O**F *= 105°

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

⇒ *`∠`**AOE *+ *`∠`**AOC *+ *`∠`**COF *= 180°

⇒ 40° + *`∠`**AOC *+105° = 180°

⇒ *`∠`**AOC *= 180° -145°

⇒ *`∠`**AOC *= 35°

Also, *`∠`**B**O**F *= *`∠`**A**O**E *= 40° [ ∵ Vertically opposite angle are equal]

Concept: Concept of Parallel Lines

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