find $m\\angle bfc$.\n$m\\angle bfc = \\square^\\circ$

Explanation:

Step1: Identify right angle and vertical angles

$\angle AFD$ is a right angle ($90^\circ$), and $\angle BFC$ and $\angle EFD$ are vertical angles? Wait, no, $\angle AFB$ and $\angle EFD$: Wait, $\angle AFD = 90^\circ$, $\angle EFD = 28^\circ$, so $\angle AFE = 90^\circ - 28^\circ = 62^\circ$? No, wait, $\angle AFD$ is $90^\circ$ (since $AF \perp FC$? Wait, $FG$ and $AC$? Wait, $AF$ is vertical, $FC$ is horizontal, so $\angle AFC = 90^\circ$. Then $\angle BFC$: since $\angle EFD = 28^\circ$, and $\angle BFC$ is equal to $\angle AFB$? Wait, no, $\angle AFD = 90^\circ$, $\angle EFD = 28^\circ$, so $\angle AFE = 90^\circ - 28^\circ = 62^\circ$? Wait, no, $\angle BFC$: let's see, $AF$ and $FD$ are perpendicular (right angle), so $\angle AFD = 90^\circ$. $\angle EFD = 28^\circ$, so $\angle AFE = 90^\circ - 28^\circ = 62^\circ$? Wait, no, $\angle BFC$: since $AB$ and $ED$ are intersecting? Wait, no, $\angle BFC$: the angle at $F$ between $B$ and $C$. Since $AF \perp FC$ (right angle), and $\angle AFB$ is equal to $\angle EFD$ (vertical angles)? Wait, $\angle EFD = 28^\circ$, so $\angle AFB = 28^\circ$? Then $\angle BFC = 90^\circ - 28^\circ = 62^\circ$? Wait, no, let's re-examine.

Wait, $FC$ is horizontal, $AF$ is vertical, so $\angle AFC = 90^\circ$. $\angle EFD = 28^\circ$, and $\angle BFC$: since $\angle AFB$ and $\angle EFD$ are vertical angles? Wait, $\angle AFB$ and $\angle EFD$: yes, because $AB$ and $ED$ intersect at $F$, so vertical angles. So $\angle AFB = \angle EFD = 28^\circ$? No, wait, $\angle AFD = 90^\circ$, so $\angle AFB + \angle BFD = 90^\circ$? No, maybe I messed up. Wait, $AF$ is vertical (up), $FD$ is vertical (down), so $AFD$ is a straight line? No, $AF$ and $FD$ are opposite rays, so $AFD$ is a straight line? Wait, no, $AF$ is up, $FD$ is down, so $AFD$ is a straight line (180°), but $\angle AFC$ is 90° (since $FC$ is horizontal). So $\angle AFD = 90^\circ$ (because $AF \perp FC$? Wait, $FG$ and $AC$: $FG$ is horizontal, $AF$ is vertical, so $\angle AFC = 90^\circ$. Then $\angle EFD = 28^\circ$, and $\angle BFC$: since $AB$ and $ED$ are intersecting, $\angle BFC$ and $\angle EFD$: no, $\angle BFC$ is adjacent to $\angle AFB$. Wait, $\angle AFB$ and $\angle EFD$ are vertical angles (because $AB$ and $ED$ intersect at $F$), so $\angle AFB = \angle EFD = 28^\circ$. Then $\angle BFC = \angle AFC - \angle AFB = 90^\circ - 28^\circ = 62^\circ$. Yes, that makes sense. So $\angle BFC = 62^\circ$.

Step2: Calculate $m\angle BFC$

Since $\angle AFC = 90^\circ$ (right angle) and $\angle AFB = \angle EFD = 28^\circ$ (vertical angles), then $m\angle BFC = 90^\circ - 28^\circ = 62^\circ$.

Answer:

$62$