KöMaL 2014 B4664

A rectangle $ABDE$ is drawn to side $AB$ of an acute triangle $ABC$ on the inside, such that point $C$ should lie on the side $DE$ . The rectangles $BCFG$ and $CAHI$ are defined in a similar way. ($A$ lies on line segment $FG$ , and $B$ lies on line segment $HI$ .) The midpoints of sides $AB$ , $BC$ , and $CA$ are $J$ , $K$ , and $L$ , respectively. Prove that the sum of the angles $GJH\sphericalangle$, $IKD\sphericalangle$ and $ELF\sphericalangle$ is $180^{\circ}$.