In Fig. 8.61, lines AB, CD and EF intersect at O . Find the measures of ∠ AOC, ∠ COF, ∠ DOE and ∠ BOF .

Question

In Fig. 8.61, lines AB, CD and EF intersect at O . Find the measures of &#x2220; AOC, &#x2220; COF, &#x2220; DOE and &#x2220; BOF .

Philoid · Accepted Answer

∠AOE + ∠EOB = 180^o(Linear pair)

∠AOE + ∠DOE + ∠BOD = 180^o

∠DOE = 105^o

∠DOE = ∠COF = 105^o(Vertically opposite angle)

∠AOE + ∠AOF = 180^o(Linear pair)

40^o + ∠AOC + 105^o= 180^o

∠AOC = 35^o

Also,

∠BOF = ∠AOE = 40^o(Vertically opposite angle)