Question

in the given figure AOB is a line determine x

Answer 1

60 +2x +60 = 180
x=30

Answer 2

FULL ANSWER WITH STEPS

In the given figure, 
∠AOP = 60°
∠POQ = $2x$
∠BOQ = 60°

Now, 
∠AOP + ∠POQ + ∠BOQ = ∠AOB
⇒ $60+2x+60=180$               [∵ ∠AOB = 180°]
⇒ $2x+120=180$
⇒ $2x=180-120$
⇒ $2x=60$
⇒ $x=\frac{60}{2}$
⇒ $x=30$

∴ $x=30$

Hope this may help you. 

If you have any doubt, then you can ask me in the comments.