1. **State the problem:** We have a circle with center $p$ and an arc $qr$ measuring 144 degrees. We need to find the degree measure of angle $pqr$. 2. **Recall the relevant rule:** The angle formed at the circumference by two points on the circle (angle $pqr$) is half the measure of the intercepted arc $qr$. 3. **Apply the formula:** $$\text{angle } pqr = \frac{1}{2} \times \text{arc } qr$$ 4. **Substitute the given value:** $$\text{angle } pqr = \frac{1}{2} \times 144$$ 5. **Calculate:** $$\text{angle } pqr = 72$$ 6. **Conclusion:** The degree measure of angle $pqr$ is 72 degrees.