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Question
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°
`∠`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.
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