1. The problem asks to identify the types of angles $\angle ABE$ and $\angle CFB$ in the given geometric figure. 2. From the description, $\angle ABE$ is an angle at vertex $B$ formed by points $A$ and $E$, and $\angle CFB$ is an angle at vertex $F$ formed by points $C$ and $B$. 3. Since $\triangle PQS \sim \triangle TQR$ by SAS similarity, corresponding angles are equal. 4. The arcs at vertices $B$ and $F$ indicate these angles are congruent. 5. Given the figure and the arcs, $\angle ABE$ and $\angle CFB$ are both acute angles because the arcs are small and less than 90 degrees. 6. Therefore, $\angle ABE$ and $\angle CFB$ are acute angles, meaning each measures less than $90^\circ$. Final answer: $\angle ABE$ and $\angle CFB$ are acute angles.