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Question

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


Solution

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
⇒ 18= 180
⇒ = 10
Therefore, 
∠BOC = 4y
= 40
∠EOD = 8y
= 80
​∠AOF = 6y
= 60
Hence, the measures of ∠BOC, ∠EOD, ∠AOF are 4080 and 80 respectively.

Mathematics
Mathematics (Solutions)
Standard VII

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