# How do you name an angle between 0^circ and 360^circ that is coterminal with the angle -210^circ?

Jul 26, 2018

$150$°

#### Explanation:

Angles that are coterminal with $- 210$° can be written in the form:
$- 210 + 360 k$ where $k$ is some integer constant.

Using intuition, we pick out a value an integer for $k$ that would result in a value that lies between $0$° and $360$°. In this case, $k$ would be $1$, but if you don't have the intuition or you have time, you can just pick out several values for $k$ that would make it lie around values between $0$° and $360$°.

Using $k = 1$:
$- 210 + 360 \left(1\right)$ = $- 210 + 360$ = $150$°

or

Using several values for $k$:
we get ...$- 930$°, $- 570$°, $- 210$°, $150$°, $510$°, $870$°...

All of these values are coterminal, but the only one that lies between $0$° and $360$° is $150$°.