Geometrically, the reference angle is the smallest angle between the terminal ray and the x-axis.
Algebraically, the reference angle for X is the smaller of (X mod 180°) and (-X mod 180°).
Here, that would be
.. min(227 mod 180, -227 mod 180)
.. = min(47, 133)
.. = 47 . . . . degrees
_____
"X mod 180" means you subtract the largest multiple of 180 that is smaller than X.
Then 227 mod 180 = 227 -180 = 47
and -227 mod 180 = -227 -(-360) = 133.
