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In the below Fig, OA and OB are opposite rays. If y = 35°, what is the value of x? - Mathematics

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Answer in Brief

In the below Fig, OA and OB are opposite rays.

If y = 35°, what is the value of x?

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Solution 1

Given that if y = 35°

`∠`AOC + `∠`BOC = 180°

(2 y + 5) + 3x = 180°

(2 (35) + 5) + 3x = 180°

(70 + 5) + 3x = 180°

3x = 180° - 75°

3x = 105°

x = 35°

x = 35°

Solution 2

In figure:

Since OA and OB are opposite rays. Therefore, AB is a line. Since, OC stands on line AB.

Thus,∠AOCand ∠BOC form a linear pair, therefore, their sum must be equal to180°.

Or, we can say that

∠AOC + ∠BOC = 180°

From the given figure:

∠AOC= (2y + 5)and ∠BOC = 3x

On substituting these two values, we get

`(2y + 5) + 3x = 180`

`3x + 2y = 180 -5`

 3x + 2y = 175                            ...(i)

On putting in y =35 in equation (A), we get:

`3x + 2(35) =175`

`3x + 70 = 175`

          `3x = 175 - 70`

           `3x = 105`

              `x = 105/3`

               `x = 35`

Hence, the value of x is 35.

Concept: Pairs of Angles
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 1.2 | Page 14

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