Answer:
m∠AOC = 37°, m∠BOF= 15°, m∠COF = 128° and m∠COE = 52°.
Step-by-step explanation:
Given: AB, CD and EF are straight lines intersecting at point O.
m∠AOE = 15° and m∠BOD = 37°
Sol: m∠AOE = m∠BOF (vertically opposite angles are equal)
∴ m∠BOF = 15°
similarly, m∠BOD = m∠AOC (vertically opposite angles are equal)
∴ m∠AOC = 37°
Now, m∠AOE + m∠EOD + m∠DOB = 180° (sum of angles on a straight line is 180°)
∴ m∠EOD = 180° - (15° + 37°) = 180° - 52° = 128°
Now, m∠EOD = m∠COF (vertically opposite angles)
∴ m∠COF = 128°
∵ m∠COE = m∠COA + m∠AOE
∴ m∠COE = 37° + 15° = 52°
∴ m∠AOC = 37°, m∠BOF= 15°, m∠COF = 128° and m∠COE = 52°.
