Question

Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Figure), find ∠COF.

Answer 1

∵ 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°