What is a Reference Angle?
The reference angle is the positive acute angle that can represent an angle of any measure.
The reference angle $$ \text{ must be } < 90^{\circ} $$
In radian measure, the reference angle $$\text{ must be } < \frac{\pi}{2} $$
Basically, any angle on the xy plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the xaxis. A reference angle always uses the xaxis as its frame of reference.
Rules of Angles and Reference angle
Positive angles go in a counter clockwise direction. Below is a picture of a positive fifty degree angle
Quadrant I
Every positive angle in quadrant I is already acute...so the reference angle is the measure of the angle itself:
Quadrant II
To find the reference angle measuring x ° for angle in Quadrant III, the formula is $$ 180  x^{\circ} $$.
Quadrant III
To find the reference angle measuring x ° for angle in Quadrant III, the formula is $$ x  180 ^{\circ} $$.
Quadrant IV
To find the reference angle measuring x ° for angle in Quadrant IV, the formula is $$360 ^{\circ} x $$.
Practice Problem
Remember that the reference angle always uses the xaxis as a frame of reference.
Remember that the reference angle always uses the xaxis as a frame of reference.
Remember that the reference angle always uses the xaxis as a frame of reference.
Word Problems
For a quadrant 2 angle, the reference angle is always 180°  given angle
In this case, $$ 180  91 = \color{Red}{89} $$
For a quadrant 3 angle, the reference angle is always given angle  180°
In this case, $$ 250  180= \color{Red}{ 70 } $$

Further Reading:
 Unit Circle Game Free online game on all things about the unit circle
 Unit Circle Printables Images of blank unit circles and blank unit circles with the answers filled in
 Unit Circle Worksheet