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Question

In the given figure, three lines AB, CD and EF intersect at a point O such that AOE=35 and BOD=40. Find the measure of AOC,BOF,COF and DOE.

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Solution

In the given figure,

∠AOC = ∠BOD = 40o (Vertically opposite angles)

∠BOF = ∠AOE = 35o (Vertically opposite angles)

Now, ∠EOC and ∠COF form a linear pair.

∴ ∠EOC + ∠COF = 180o

⇒ (∠AOE + ∠AOC) + ∠COF = 180o

⇒ 35o + 40o + ∠COF = 180o

⇒ 75o + ∠COF = 180o

⇒ ∠COF = 180o − 75o = 105o

Also, ∠DOE = ∠COF = 105o

(Vertically opposite angles)


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