That means 1/2angleAOB=angleAOC=angleCOB

rayOD bisects angleAOC:

that means 1/2angleAOC=angleAOD=angleDOC

rayOE bisects angle AOD:

that means 1/2angleAOD=angleAOE=angleEOD

rayOF bisects angle AOE:

that means 1/2angleAOE=angleAOF=angleFOE

rayOG bisects angle FOC:

that means 1/2angleFOC=angleFOG=angleGOC

let x=angleAOF=angleFOE

then 2x=angleAOE=angleEOD

then 4x=angleAOD=angleDOC

then 8x=angleAOC=angleCOB

120 = angleBOF= angleFOB =

angleFOE + angleEOD + angleDOC + angleCOB

120 = x + 2x + 4x + 8x

120 = 15x

8 = x

angleDOE = angle EOD = 2x = 16

if angle COG=35, the angleEOG=?

rayOG bisects angleFOC,

that means 1/2angleFOC=angleFOG=angleGOC

angleFOC= angleFOE + angleEOD + angleDOC

angleFOC= x + 2x + 4x = 7x

and

angleFOG=angleGOC=3.5x

angleEOG = angleEOB -(angleGOC+angleCOB)

angleEOG = (angleEOC+angleCOB) -(3.5x+angleCOB)

angleEOG = (angleEOC-3.5x) + (angleCOB-angleCOB)

angleEOG = (angleEOD+angleDOC-3.5x)

angleEOG = (2x+4x – 3.5x)= 2.5x = 2.5(8) = 20