Question

Given: m∠AOC = 120°, m∠BOD = 150°. Find: m∠FOE.

Answer 1

In the finding of m<FOE, I think it would be 70°.

Answer 2

∠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.