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In the Below Fig, Lines Ab, Cd and Ef Intersect at O. Find the Measures of ∠Aoc, ∠Cof, ∠Doe and ∠Bof. - Mathematics

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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

`∠`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]

Concept: Concept of Parallel Lines
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.3 | Q 7 | Page 23

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