Find the reference angle for a rotation of 242 degrees.

1. Identify the quadrant: The angle $242^\circ$ is greater than $180^\circ$ and less than $270^\circ$. This means the angle lies in the third quadrant.

1. Determine the reference angle formula for the third quadrant: In the third quadrant, the reference angle is found by subtracting $180^\circ$ from the given angle. The formula is: Reference Angle = $\theta - 180^\circ$, where $\theta$ is the given angle.

3. Calculate the reference angle: Substitute the given angle $242^\circ$ into the formula:
Reference Angle = $242^\circ - 180^\circ$
Reference Angle = $62^\circ$