OC bisects AOB, OD bisects AOC, OE bisects AOD, OF bisects AOE, OG bisects BOF. if BOF =120°, find DOE

∠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°.

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