I need help finding the reference for these given angles... I need help finding the reference for these given angles...
(a) 120° 
(b) -210° 
(c) 780° 
 A: The reference angle can be defined in various ways. One way is as follows: the reference angle is the acute angle formed by the terminal side of the given angle, and the $x$-axis, which was mentioned in the comments. You can play around with this visually on the coordinate plane to get a nice generalization:
Suppose $\theta$ is an angle, from $0^{\circ}$ to $360^{\circ}$.
$\bullet$ If $\theta$ is in the first quadrant, then the reference is itself, $\theta$.
$\bullet$ If $\theta$ is in the second quadrant, the reference is $180^{\circ} - \theta$.
$\bullet$ If $\theta$ is in the third quadrant, the reference is $\theta - 180^{\circ}$.
$\bullet$ If $\theta$ is in the fourth qudrant, the reference is $360^{\circ} - \theta$.
Now, $120^{\circ}$ is in the second quadrant, so it's reference angle would be $\ldots$
For your other two angles, they are less than $0^{\circ}$ or greater than $360^{\circ}$. Thus, you have to find the angle from $0^{\circ}$ to $360^{\circ}$ that coincides with each of them. To do this, you add or subtract $360^{\circ}$ until you get an angle that is between $0^{\circ}$ to $360^{\circ}$.
$-210^{\circ} + 360^{\circ} = 150^{\circ}$, and since $150^{\circ}$ is in the second quadrant, the reference of $-210^{\circ}$ is $\ldots$
$780^{\circ} - 360^{\circ} - 360^{\circ} = 60^{\circ}$, and since $60^{\circ}$ is in the first quadrant, the reference of $780^{\circ}$ is $\ldots$
