The reference angle is always the angle between the line made by the given angle, theta, and either the +x or -x axis depending on which gives you the smaller angle. In fact, a reference angle is always an acute angle or a right angle. Also, a reference angle is always considered to be positive.Originally Posted bymelissa

So. 195 degrees is in the third quadrant, just under the -x axis. The reference angle is thus 195 - 180 = 15 degrees.

120 degrees is in the second quadrant. So the reference angle is 180 - 120 = 60 degrees.

Two last examples:

42 degrees. If an angle is in the first quadrant, the angle is its own reference angle, so the reference angle here is 42 degrees. (If you like, the angle is above the +x axis, so 42 - 0 = 42 degrees.)

315 degrees. This is a fourth quadrant angle, so it is below the +x axis. Thus 360 - 315 = 45 degrees is the reference angle.

-Dan