Question

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

Answer 1

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°.