1. **Problem Statement:** We have a circle with center $P$ and points $A, B, C, D, E$ on the circle in clockwise order. $\overline{AD}$ and $\overline{BE}$ are diameters. We want to find the measure of the minor arc $\stackrel{\large{\frown}}{CD}$ in degrees. 2. **Given Information:** - $\angle APE = 90^\circ$ (right angle) - $\angle DPE = (33k - 9)^\circ$ - $\angle CPD = (20k + 4)^\circ$ 3. **Key facts:** - Diameters $AD$ and $BE$ imply $A, D$ are opposite points and $B, E$ are opposite points on the circle. - Central angles correspond to arc measures. - The sum of all central angles around point $P$ is $360^\circ$. 4. **Find $k$:** Since $\angle APE = 90^\circ$, and $A, P, E$ are points on the circle with $A$ and $E$ on diameters, the arcs between these points relate to the angles given. 5. **Sum of central angles:** The central angles around $P$ are $\angle APE$, $\angle DPE$, $\angle CPD$, and the remaining angle(s) to complete $360^\circ$. 6. **Calculate $k$ using the sum of angles:** $$90 + (33k - 9) + (20k + 4) + x = 360$$ where $x$ is the remaining angle(s). 7. **Simplify:** $$90 + 33k - 9 + 20k + 4 + x = 360$$ $$33k + 20k + (90 - 9 + 4) + x = 360$$ $$53k + 85 + x = 360$$ 8. **Since $x$ is the remaining angle, and all angles sum to 360, $x$ must be positive. But we only need $k$ to find $\angle CPD$. Let's assume $x$ is the angle $\angle BPC$ (not given), so we cannot solve for $k$ directly without more info. However, the problem likely expects us to find the arc measure of $\stackrel{\large{\frown}}{CD}$ which equals $\angle CPD$. 9. **Therefore, the arc measure of minor arc $\stackrel{\large{\frown}}{CD}$ is:** $$\boxed{20k + 4}$$ degrees. Since no value of $k$ is given or can be found from the data, the answer is expressed in terms of $k$.