#### 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 x-y 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 **x-axis**. A reference angle always uses the x-axis 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 $$360 ^{\circ} -x $$.