To find the reference angle for $-350^\circ$, we first need to determine the equivalent positive angle by adding $360^\circ$ until the angle is within the range of $0^\circ$ to $360^\circ$.

Step-by-Step Solution:

1. Normalize the Angle to $0^\circ$ to $360^\circ$:

   $-350^\circ + 360^\circ = 10^\circ$

   The equivalent angle within the range of $0^\circ$ to $360^\circ$ is $10^\circ$.

2. Determine the Reference Angle:

   The reference angle is the acute angle formed with the x-axis. Since $10^\circ$ is already between $0^\circ$ and $90^\circ$, it is in the first quadrant. For angles in the first quadrant, the reference angle is the angle itself.

   $\text{Reference angle} = 10^\circ$

Conclusion:

The reference angle for $-350^\circ$ is $\boxed{10^\circ}$.

Would you like more details or have any questions about the solution? Here are some related questions:

1. What is the reference angle for $-180^\circ$?
2. How do you find the reference angle for angles in different quadrants?
3. What is the equivalent angle of $-700^\circ$ within the range $0^\circ$ to $360^\circ$?
4. How is the reference angle used in trigonometry?
5. What are the steps to find the reference angle of an angle greater than $360^\circ$?

Tip: Remember that a reference angle is always a positive acute angle between $0^\circ$ and $90^\circ$.