Question

In the given figure, lines AB, CD and EF intersect at O. Find the measure of ∠COF

Answer 1

Given

∠AOE = 400 & ∠BOD = 350

Clearly ∠AOC = ∠BOD [Vertically opposite angles]

⇒ ∠AOC = 350 Ans.

∠BOF = ∠AOE [Vertically opposite angles]

⇒ ∠BOF = 400 Ans.

Now, ∠AOB = 1800 [Straight angles]

⇒ ∠AOC + ∠COF + ∠BOF = 1800 [Angles sum property]

⇒ 350 + ∠COF + 400 = 1800

⇒ ∠COF = 1800 - 750 = 1050

Now, ∠DOE = ∠COF [Vertically opposite angles] ∴ ∠DOE = 1050

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Answer 2

Answer:

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AOE = 400 & ∠BOD = 350

Clearly ∠AOC = ∠BOD [Vertically opposite angles]

⇒ ∠AOC = 350 Ans.

∠BOF = ∠AOE [Vertically opposite angles]

⇒ ∠BOF = 400 Ans.

Now, ∠AOB = 1800 [Straight angles]

⇒ ∠AOC + ∠COF + ∠BOF = 1800 [Angles sum property]

⇒ 350 + ∠COF + 400 = 1800

⇒ ∠COF = 1800 - 750 = 1050

Now, ∠DOE = ∠COF [Vertically opposite angles] ∴ ∠DOE = 1050

❣️