# How do you find the reference angle of #theta=-245^circ# and sketch the angle in standard position?

##### 1 Answer

The reference angle is 65°.

#### Explanation:

Assuming an angle is in standard position, its **reference angle** is the smallest angle you can make between the terminal ray and the whole left-right

Mathematically, the reference angle is the **difference between the angle and the closest multiple of 180°.**

#theta_"ref" = min{abs(theta-180n°):n in ZZ}#

An angle of

Thus, the closest multiple of 180° to

The difference between these two is

#abs(–245° - (–180°))#

#=abs(–245°+180°)#

#=abs(–65°)#

#=65°#

### Visual shortcut:

Draw the angle