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

Apr 26, 2018

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 $x$-axis.

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 theta = –245° lies in Quadrant II.
Thus, the closest multiple of 180° to $\theta$ is –180°.
The difference between these two is

abs(–245° - (–180°))
=abs(–245°+180°)
=abs(–65°)
=65°

### Visual shortcut:

Draw the angle $\theta$, then picture folding the plane in half, with the crease on the $x$-axis. Bend the two halves up. The reference angle is the angle that $\theta$ travels through if it were to fall towards the $x$-axis.