Question

Solve the problems. Show your work with proper statements and notation. b AB , CD and EF are straight lines intersecting at point O. Find m∠AOC, m∠BOF, m∠COF, m∠COE. This will be my last question for the day thanks.

Answer 1

here is answer!

Explanation:

AOC=37

BOF=15

COF=128

COE=52

Answer 2

m∠AOC = 37°, m∠BOF= 15°, m∠COF = 128° and m∠COE = 52°.

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°.