In the below Fig. OA and OB are opposite rays:
Question:

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

(i) If x = 25, what is the value of y?

(ii) If y = 35, what is the value of x?

Solution:

(i) Given that,

x = 25

Since ∠AOC and ∠BOC form a linear pair

∠AOC + ∠BOC = 180°

Given that ∠AOC = 2y + 5 and ∠BOC = 3x

∠AOC + ∠BOC = 180°

(2y + 5) + 3x = 180

(2y +5) + 3(25) = 180

2y + 5 + 75 = 180

2y + 80 = 180

2y = 180 – 80 = 100

y = 100/2 = 50

y = 50

(ii) Given that,

y = 35

∠AOC + ∠BOC = 180°

(2y + 5) + 3x = 180

(2(35) + 5) + 3x = 180

(70 + 5) + 3x = 180

3x = 180 – 75

3x = 105

x = 35

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