2020 AIME II Problem 4

Triangles \triangle ABC and \triangle A'B'C' lie in the coordinate plane with vertices A(0,0), B(0,12), C(16,0), A'(24,18), B'(36,18), C'(24,2). A rotation of m degrees clockwise around the point (x,y) where 0<m<180, will transform \triangle ABC to \triangle A'B'C'. Find m+x+y.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.