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.

Answer 1

It is given that ∠BOD = 40^o

From the figure we know that ∠BOD and ∠AOC are vertically opposite angles

∠AOC = ∠BOD = 40^o

It is given that ∠AOE = 35^o

From the figure we know that ∠BOF and ∠AOE are vertically opposite angles

∠AOE = ∠BOF = 35^o

From the figure we know that AOB is a straight line

So it can be written as

∠AOB = 180^o

We can write it as

∠AOE + ∠EOD + ∠BOD = 180^o

By substituting the values

35^o + ∠EOD + 40^o = 180^o

On further calculation

∠EOD = 180^o – 35^o – 40^o

By subtraction

∠EOD = 105^o

From the figure we know that ∠COF and ∠EOD are vertically opposite angles

∠COF = ∠EOD = 105^o