In the below fig. lines AB. CD and EF intersect at O. Find the measures of ∠AOC, ∠COF, ∠DOE and ∠BOF.
Question:
In the below fig. lines AB. CD and EF intersect at O. Find the measures of ∠AOC, ∠COF, ∠DOE and ∠BOF.
Solution:
AOE and EOB are linear pair of angles
∠AOE + ∠EOB = 180°
∠AOE + ∠DOE + ∠BOD = 180°
⟹ DOE = 180 - 40 - 35 = 105
Vertically opposite side angles are equal
DOE = COF =105
Now, ∠AOE + ∠AOF = 180°
[Linear pair]
AOE + AOC + COF = 180
⟹ 40 + AOC +105 = 180
⟹ AOC = 180 - 145
⟹ AOC = 35
Also, BOF = AOE = 40 (Vertically opposite angles are equal)