To find the reference angle for 563 degrees, first, we can subtract 360 degrees from it since it exceeds one full rotation. This gives us 563 - 360 = 203 degrees. The reference angle is then found by subtracting this angle from 360 degrees if it lies in the third quadrant, resulting in 203 - 180 = 23 degrees. Therefore, the reference angle for 563 degrees is 23 degrees.
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