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Question
Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Figure), find ∠COF.
Solution
∵ AB is a straight line.
∴ ∠AOE + ∠EOD + ∠DOB = 180°
⇒ ∠EOD = 180° – 30° – 40° = 110° ......(i) [∵∠AOE = 30° and ∠DOB = 40° (given)]
Now, CD and EF intersect each other at O.
∴ ∠COF = ∠EOD = 110° ......[Using (i)] [Vertically opposite angles]
Thus, ∠COF = 110°
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