#### Question

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

If x = 25°, what is the value of y?

#### Solution 1

Given that *x *= 25°

Since *`∠`**A**O**C *and *`∠`**B**O**C *form a linear pair

*`∠`A**O**C *+ *`∠`**B**O**C *= 180°

Given that

*`∠`AOC *= 2 *y *+ 5 and *`∠`**B**O**C *= 3*x*

*∴ `∠`A**O**C *+ *`∠`**B**O**C *= 180°

(2 *y *+ 5)° + 3*x *= 180°

(2 *y *+ 5)° + 3(25°) = 180°

2 *y*° + 5° + 75° = 180°

2 *y*° + 80° = 180°

2 *y*° = 180° - 80° = 100°

*y*° = `(100°)/2` = 50°

⇒ *y *= 50°

#### 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 x = 25in (i), we get:

`3(25 )+2y = 175`

`75 + 2y = 175`

`2y = 175 - 75`

`2y = 100`

`y = 100/2`

`y = 50`

Hence, the value of *y* is 50.