Question

O is the centre of the circle.find x

Answer 1

angle AOC = 180-60=120 (Linear pair)
and OC=OA=x
then,
in triangle OCA,
x+x+120=180 (angle sum property of triangle)
2x=180-120
x=60/2=30..

Answer 2

If BC is diameter than 
<AOC+<AOB=180
<AOC+60=180
<AOC=120             (180-60=120)

OA=OC      (radii of same circle)
<OAC=<OCA=X    (angles opposite to equal sides are equal)

<OAC+<OCA+<AOC=180
X+X+120=180
2X=60
X=60/2
X=30