# How do you find the reference angle for the given angle 415?

A reference angle is the angle between the X-axis and the arm of some given angle and is always measured as a value in the range $\left[0 , \frac{\pi}{2}\right]$ or (equivalently) $\left[0 , {90}^{\circ}\right]$
Assuming your $415$ is meant to be ${415}^{\circ}$ (and not radians):
$\textcolor{w h i t e}{\text{XXXX}}$${415}^{\circ} = {360}^{\circ} + {55}^{\circ}$
The reference angle is ${55}^{\circ}$