Check the picture below.
notice that the point A is the center of the circle, and thus the ∡BAF is a central angle, and the arc BF gets its angle measurement from ∡BAF, in red.
now, notice, ∡BAF has a twin vertical angle, namely ∡CAE in green, and the arc made by ∡CAE is congruent to BF.
notice that the point A is the center of the circle, and thus the ∡BAF is a central angle, and the arc BF gets its angle measurement from ∡BAF, in red.
now, notice, ∡BAF has a twin vertical angle, namely ∡CAE in green, and the arc made by ∡CAE is congruent to BF.