Iwill award ab , cd and ef are straight lines intersecting at point o. find m∠aoc, m∠bof, m∠cof, m∠coe.

The measure of m∠AOC, m∠BOF, m∠COF, and m∠COE are 37, 15, 128, and 52degrees respectively.

The point where two lines meet is known as an angle

From the diagram given:

m<AOE + m<EOD + m<DOB = 180

15 + m<EOD + 37 = 180

m<EOD = 180 - 52

m<EOD = 128 degrees

From the diagram m<DOB = m<AOC = 37 degrees (vertical angles)

m∠BOF = m∠AOE = 15 degreed (vertical angles)

m∠COF = m∠EOD = 128 degrees (vertical angles)

m∠COE = m∠COA + m∠AOE

m∠COE = 15 + 37

m∠COE = 52 degrees

Hence the measure of m∠AOC, m∠BOF, m∠COF, and m∠COE are 37, 15, 128, and 52degrees respectively.

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angle EOD

180 = AOE + EOD + DOB

180 = 15 + EOD + 37

180 = 52+EOD

subtract 52 from each side

EDO = 128

COF

COF = 128  vertical angles  (EDO)

AOC

AOC =37  vertical angles  (DOB)

BOF

BOF = 15  vertical angles (EOA)

COE

COE = COA+AOE

         =37+15

        = 52