Sorry for my bad grammar:
ABCD is a square and BDE is a right triangle where the angle BED is the right angle and ACF is BDE but rotated(They have the same angles and side lengths and AFC is the right angle) and a line connects E and F and it is NOT the bisector. What's the difference between the angles E1 and F1? The shape:
Draw the circle of diameter $AC$: point $F$ belongs to it (you should know why) and the center $O$ of the square also lies on it.
But line $EF$, by symmetry, passes through $O$. Hence inscribed angles $\angle AFO$ and $\angle CFO$ both subtend a quarter of the circle and are thus congruent. The same applies to $\angle DEO$ and $\angle BEO$.
Here's a diagram made with GeoGebra. Notice that triangle $BED$ is obtained by rotating $ACF$ by $180°$ about $O$, hence line $EF$ passes through $O$. If $BED$ were oriented the other way, then it couldn't be a rotated copy of $ACF$, as stated in the question.