2020 AIME II Problem 4

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