Question

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

If x = 25°, what is the value of y?

Answer 1

Given that x = 25°

Since `∠`AOC and `∠`BOC form a linear pair

`∠`AOC + `∠`BOC = 180°

Given that

`∠`AOC = 2 y + 5 and `∠`BOC = 3x

∴ `∠`AOC + `∠`BOC = 180°

(2 y + 5)° + 3x = 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°

Answer 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.