Question

Using the measures of the angles given in the figure alongside, find the measures of the remaining three angles.

Answer 1

In the given figure,
∠BOC = ∠FOE = 4y (Vertically opposite angles)
∠EOD = ∠AOB = 8y (Vertically opposite angles)
∠AOF = ∠COD = 6y (Vertically opposite angles)
Now, ∠AOB + ∠BOC + ∠COD = 180^∘ (Linear Pair angles)
⇒ 8y + 4y + 6y = 180^∘
⇒ 18y = 180^∘
⇒ y = 10^∘
Therefore,
∠BOC = 4y
= 40^∘
∠EOD = 8y
= 80^∘
​∠AOF = 6y
= 60^∘
Hence, the measures of ∠BOC, ∠EOD, ∠AOF are 40^∘, 80^∘ and 80^∘ respectively.