In the given figure, PQ \ \ MN. Find the value of x.

Through O, draw AB || PQ || MN

∵ AB || PQ

∴ ∠1 = 30°

also,AB|| MN

then ∠2= 40° [alternate interior angles]

Now,∠x+∠1+∠2=360°[angles around a point]

⇒ x=360°-(∠1+∠2)

⇒ x = 360°-(30°+40°)

⇒ x = 290°