In Fig. 8.31, 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 ?

Question

In Fig. 8.31, OA and OB are opposite rays: (i) If x = 25&#xB0;, what is the value of y ? (ii) If y = 35&#xB0;, what is the value of x ?

Philoid · Accepted Answer

(i) Given that,

x = 25^o

∠AOC + ∠BOC = 180^o (Linear pair)

(2y + 5) + 3x = 180^o

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

2y = 100^o

y = 50^o

(ii) Given that,

If y = 35^o

∠AOC + ∠BOC = 180^o

(2y + 5) + 3x = 180^o

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

3x = 105^o

x = 35^o