Given: m∠aoc = 120°, m∠bod = 150°. find: m∠foe.

∠FOE = 90°

Step-by-step 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.

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step-by-step explanation: