Question

In the figure, lines AB, CD and EF intersect at O. Find the measures of
angle AOE, angle EOD, angle BOD and angle COF.​

Answer 1

Step-by-step explanation:

It is given that ∠BOD=180o

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

∠AOC=∠BOD=40o

It is given that ∠AOE=35o

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

∠AOE=∠BOF=35o

from the figure, we know that AOB is a straight line

so it can be written as

∠AOB=180o

we can write it as

∠AOE+∠EOD+∠BOD=180o

by substituting the values

35o+∠EOD+40o=180o

∠EOD=105o

from the figure, we know that ∠COF and ∠EOD are 

vertically opposite angles

∠COF=∠EOD=105o