In the given figure, three lines AB, CD and EF intersect at a point O such that ∠AOE = 35° and ∠BOD = 40°.
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.

 

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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