theorems

[violet vector]

AO and OC both have the length of the radius of the circle. Hence the triangle is isosceles which means x = w(ACO) = w(OAC). Since AOC is a triangle we get x + w(ACO) + w(OAC) + w(AOC) = 2x+w(AOC)= 180 which leads to w(AOC)=180-2x

[subtle pine]

Thanks