let the centre of the circle be O

let angle COX(major) be 2x

angle CBX = 0.5 angle COX(major) = x

(angle of circumference is 1/2 of the angle at centre)

angle COX ( minor) + angle COX(major) = 360 (angel at a point)

thereofre angle COX (minor) = 360 -2x

angle CYX = 0.5 angle COX(minor) = 180 -x

(angle of circumference is 1/2 of the angle at centre)

so angle CBX + angle CYX = x + 180 -x = 180 (proven)