\&. Find the reference angle for the angle \( 865^{\circ} \) The reterence angle is \( \square^{\circ} \)

To find the reference angle for \( 865^\circ \), we first need to reduce this angle to an equivalent angle within the range of \( 0^\circ \) to \( 360^\circ \). 1. **Find the equivalent angle**: We can do this by subtracting \( 360^\circ \) from \( 865^\circ \) until we get an angle within the desired range. \[ 865^\circ - 360^\circ = 505^\circ \] \[ 505^\circ - 360^\circ = 145^\circ \] So, \( 865^\circ \) is equivalent to \( 145^\circ \). 2. **Determine the reference angle**: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. Since \( 145^\circ \) is in the second quadrant, we can find the reference angle by subtracting it from \( 180^\circ \): \[ \text{Reference angle} = 180^\circ - 145^\circ = 35^\circ \] Thus, the reference angle for \( 865^\circ \) is \( \boxed{35^\circ} \).