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