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Answer:
∠DOE = 16°
Step-by-step explanation:
The given parameters are;
∠BOF = 120°
∠AOB = 2×∠AOC Given
∠AOC = 2×∠AOD Given
∠AOD = 2×∠AOE Given
∠AOE = 2×∠AOF Given
Therefore;
∠AOB = 16×∠AOF Angle addition postulate
∠BOF = ∠AOB - ∠AOF = 16×∠AOF - ∠AOF = 15×∠AOF Transitive property
15×∠AOF = 120°
∠AOF = 120°/15 = 8°
Given that OE bisects ∠AOD, we have;
∠AOE ≅ ∠DOE Angles bisected by a line
From;
∠AOE = 2×∠AOF, we have; Given
Therefore;
∠AOE = ∠DOE = 2×∠AOF = 2×8° = 16°
∠DOE = 16°.