Maths on a Mug 2

This is a classic Martin Gardner puzzle. One solution is:

Construct the additional squares indicated by dotted lines. Angle C is the same as the sum of angles A and D, since they are both made by cutting a square in half along the diagonal. Angle B equals angle D because they are corresponding angles of similar right triangles (made by cutting a rectangle made from two squares in half along the diagonal). That means B can be substituted for D, which automatically makes the C equals the sum of A and B.