Question

three lines AB,CD and EF intersects each other at O. angle AOE =30 degree and angle DOB = 40 degree. find angle COF.

Answer 1

As angleEOA=angleBOF=30°[vertical opposite angle]
also,angleFOD=10°
EF is a line
angleEOF=Angle(EOA +AOD+DOF)
180°=30°+angleAOD+10°
angle AOD=180°-40°
angleAOD=140°
angleAOD=angleCOB=140°[vertical opposite angle]
angleCOF=angleCOB+angleBOF
=140°+30°
=170°

Answer 2

Given, 
∠AOE = 30°
∠DOB = 40°


So, ∠EOD = 180 - (30+40)           [angles on a straight line]
                 =  180 - 70
                 =  110

∠EOD = ∠COF                             [ vertically opposite angle]

∴ ∠COF = 110°

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Figure in the attached pic.

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Hope it is helpful....