A 4-gon A, B, C, D is inscribed in the circle. Angle B is 60 degrees. Find the angle D.

For inscribed polygons in a circle, the length of the arc on which the angle rests = 2 * the value of this angle, it follows from this:
angle B rests on an arc, which is equal to 2 * angle B = 2 * 60 = 120.
In a circle of 360 degrees, the angle D rests on an arc that will be 360 – 120 = 240, then the angle D itself will be equal to 240/2 = 120.