Question

find the reference angle for the angle 685°. the reference angle is °.

Explanation:

Step1: Find a coterminal angle

Subtract 360° from 685° until we get an angle between 0° and 360°.
$685^{\circ}-360^{\circ}=325^{\circ}$

Step2: Determine the reference - angle

Since 325° is in the fourth - quadrant (270° < 325° < 360°), the reference angle $\theta_{r}$ is given by $360^{\circ}-\theta$, where $\theta = 325^{\circ}$.
$\theta_{r}=360^{\circ}-325^{\circ}=35^{\circ}$

Answer:

$35$