1. **State the problem:** We have a circle centered at point $P$ with points $A$, $B$, $C$, $D$, and $E$ on the circumference. 2. Given that $\overline{AD}$ and $\overline{BE}$ are diameters, they each subtend straight $180^\circ$ arcs. 3. The problem provides angles at the center $P$: $\angle APE = 90^\circ$, $\angle DPE = 33K - 9^\circ$, and $\angle CPD = 20K + 4^\circ$. 4. We want to find the arc measure of the minor arc $\stackrel{\large{\frown}}{CD}$, which equals the central angle $\angle CPD$ in degrees. 5. Since we don't have $K$, let's use all center angles around $P$ that sum to $360^\circ$. The full circle is $360^\circ$ so: $$ 90 + (33K - 9) + (20K + 4) + \text{other angles} = 360 $$ 6. Sum the known angles: $$ 90 + 33K - 9 + 20K + 4 = 90 - 9 + 4 + 33K + 20K = 85 + 53K $$ 7. So the remaining angles sum to: $$ 360 - (85 + 53K) = 275 - 53K $$ 8. Without complete information to solve for $K$, typically $K$ is such that angles fit correctly, but since the problem explicitly defines $\angle CPD = 20K +4$, the arc measure of minor arc $\stackrel{\large{\frown}}{CD}$ is: $$\boxed{20K + 4}$$ degrees. Hence, the measure of minor arc $\stackrel{\large{\frown}}{CD}$ is $20K + 4$ degrees, as it equals the central angle $\angle CPD$.