Question

In the following fig oa and ob are
opposite rays
if x 25, what is the value of y?
if y = 35, what is the value of x
​

Answer 1

Figure:-

Given:-

• OA and OB are opposite rays.
• x = 25 and y = 35

To find:-

• The value of y ?
• The value of x ?

Solutions:-

• OA and OB are opposite rays.

Therefore,

AB is a line. OC stands on line AB.

Thus,

<AOC and <BOC from a linear pair.

Therefore,

Sum must be equal to 180°.

<AOC + <BOC = 180°

<AOC = (2y + 5) and <BOC = 3x

On substitution the two values, we get.

(2y + 5) + 3x = 180°

3x + 2y + 5 = 180°

3x + 2y = 180° - 5

3x + 2y = 175° .................(i).

(i). On the putting x = 25 in Eq. (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.

(ii). On the putting y = 35 in Eq. (i), 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.