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?

Answer 1

(i) Given: x = 25 

From figure: ∠AOC and ∠BOC form a linear pair 

Which implies, ∠AOC + ∠BOC = 180° 

From the figure, ∠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 = 100° 

y = 100/2 

y = 50° 

Therefore, y = 50°.

(ii) Given: y = 35° 

From figure: ∠AOC + ∠BOC = 180° (Linear pair angles) 

(2y + 5) + 3x = 180° 

(2(35) + 5) + 3x = 180°

75 + 3x = 180° 

3x = 105°

x = 35° 

Therefore, x = 35°