<Tri-2025-2211>, hint

 Let N be the midpoint of AB, then MNR is isosceles. Let <ABE=x 

Bisector of <AEB cuts MR in Q. In quadrilateral CEQR , by angle chasing. 

<QRC=180-(C+1/2(A+x))

<EQR=1/2(A+B+C)=90.