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

= 4 × 10^∘

= 40^∘

∠EOD = 8y

= 8 × 10^∘

= 80^∘

​∠AOF = 6y

= 6 × 10^∘

= 60^∘

Hence, the measures of ∠BOC, ∠EOD, ∠AOF are 40^∘, 80^∘ and 60^∘ respectively.