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Questions & Answers

CBSE

Mathematics

Grade 9

Lines and Angles

Question

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In the given figure, find the value of y.

Answer

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Hint: We can use the property of vertically opposite angles are equal to find the unknown angles. Then we can add all the angles around the point and equate it to 360∘. Then we can solve for y to get the required solution.

Complete step by step answer:

We are given that ∠AOB=6y. Consider the line AD and EB. Then, ∠AOB and ∠EODare vertically opposite angles. We know that vertically opposite angles are equal.

⇒∠AOB=∠EOD=6y… (1)

Consider the lines FC and EB. Then, ∠FOEand ∠BOC are vertically opposite angles and are equal.

⇒∠FOE=∠BOC

We know that ∠FOE=4y,

⇒∠BOC=∠FOE=4y… (2)

Now consider the lines AD and CF. Then, ∠FOAand ∠DOC are vertically opposite angles and are equal.

⇒∠FOA=∠DOC

We know that ∠DOC=8y,

⇒∠FOA=∠DOC=8y… (3)

Now we have the measures of all the angles around the point O. The sum of these angles will be 360∘ as it completes a full TURN around point O.

⇒∠AOB+∠BOC+∠COD+∠DOE+∠EOF+∠FOA=360∘

Using EQUATIONS (1), (2), and (3), we get,

6y+4y+8y+6y+4y+8y=360∘

⇒36y=360∘

Dividing throughout with 36, we get,

y=360∘36⇒y=10∘

Therefore, the required value of y is 10∘