Answer:
∠FOE = 90°
Explanation:
In this question given is m∠AOC = 120°, m∠BOD = 150°.
We have to calculate ∠FOE.
Since ∠AOB + ∠COD + ∠BOC = 180° [ Angle at a point on a straight line ]
∠AOB + ∠COD = 180° - ∠BOC ---(1)
It is given ∠AOC = 120° = ∠AOB + ∠BOC -----(2)
and ∠BOD = 150° = ∠BOC + ∠COD ------(3)
By adding equation (2) and (3)
150 + 120 = ∠ BOC + ∠COD + ∠AOB + BOC
270 = 2∠BOC + ∠COD + ∠ AOB
Now from equation (1)
270 = 2∠BOC + (180 - ∠BOC)
270 = 180 + ∠BOC
270 -180 = ∠BOC
∠BOC = 90°
Since ∠ BOC ≅ ∠FOE (opposite angles)
Therefore, ∠FOE = 90° is the answer.