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

If y = 35°, what is the value of x?

#### Solution 1

Given that if *y *= 35°

`∠`*A**O**C *+ `∠`*B**O**C *= 180°

(2 *y *+ 5) + 3*x *= 180°

(2 (35) + 5) + 3*x *= 180°

(70 + 5) + 3*x *= 180°

3*x *= 180° - 75°

3*x *= 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.