To find the reference angle of $200^\circ$, follow these steps:

1. Determine which quadrant the angle is in:

   • Angles between $180^\circ$ and $270^\circ$ lie in the third quadrant.
   • Since $200^\circ$ is between $180^\circ$ and $270^\circ$, it is in the third quadrant.

2. Calculate the reference angle: The reference angle in the third quadrant is found by subtracting the given angle from $180^\circ$. This formula is: $\text{Reference angle} = \theta - 180^\circ$ So: $\text{Reference angle} = 200^\circ - 180^\circ = 20^\circ$

Thus, the reference angle for $200^\circ$ is $\boxed{20^\circ}$.

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Would you like further details on reference angles or any other questions? Here are some related questions to explore:

1. How do you find the reference angle for angles in other quadrants?
2. What is the reference angle for $350^\circ$?
3. How do reference angles relate to trigonometric functions?
4. How do you convert a negative angle to its reference angle?
5. What is the reference angle for $45^\circ$?

Tip: For angles greater than $360^\circ$, subtract $360^\circ$ to find the equivalent angle in the first revolution before applying the reference angle method.