Explanation:
1. ∠EBC = x (Theorem One: The angle at the centre of the circle is twice the angle at the circumference subtended on the same arc. You already have this one labelled)
2. ∠FCD = x (F rule / corresponding angles are equal)
3. ∠CAE = x (Theorem Two: Angles at the circumference subtended by the same arc are congruent)
4. ∠BED = ∠DCF = ∠FCD = x (Theorem Fifteen: The exterior angle of a cyclic quadrilateral is congruent to the interior opposite angle)
5. ∠CDF = ∠BED = x (F rule / corresponding angles are equal)
6. ∠CAE = ∠OAE = ∠OEA = x (CAE and OAE are the same angles, OF and OA are radii, thus they must both be equivalent in magnitude, therefore making the triangle ΔAOE isosceles. Base angles of an isosceles triangle are always equal, since we knew ∠OAE from '3.' was x, we found that ∠OEA was also x)