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Look at the figure given alongside. Which of the following measures is different from the others? (a) Measure of 2 (b) Measure of 3 (c) Measure of 6 (d) Measure of 5​

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rekhaasantan

Answer:

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

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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∘

⇒ 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.

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