The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Given ∠ABC=50∘,
∴∠AOC=2 ∠ABC=2×50∘=100∘
Also, since OA and OC are radii of the circle, OA = OC.
⟹∠OAC=∠OCA
In △AOC,
x+x+∠AOC=180∘
⟹2x=180∘−∠AOC=180∘−100∘=80∘
⟹x=40∘