jmc

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