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°.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

c

step-by-step explanation: