1. **State the problem:** We need to find the measure of angle $\angle RAT$ formed by lines $AR$ and $AT$ using the protractor. 2. **Understand the protractor readings:** The protractor is centered at point $A$. The line $AR$ points horizontally to the right and is marked as $0^\circ$. 3. **Identify the angle:** The line $AT$ is marked at $30^\circ$ on the protractor. 4. **Calculate the angle:** Since $AR$ is at $0^\circ$ and $AT$ is at $30^\circ$, the angle $\angle RAT$ is simply the difference between these two readings. $$\angle RAT = 30^\circ - 0^\circ = 30^\circ$$ 5. **Conclusion:** The measure of angle $\angle RAT$ is $30$ degrees.