What is an angle between 0° and 360° that is coterminal with -86°?

Solution:

Coterminal angles are angles in standard positions (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, -330°, and 390° are all coterminal.

The angle -86° is in the fourth quadrant. The next angle that will coincide with the ray shown below will be 

The coterminal angle for -86° between 0° and 360° is 360° - 86° = 274°.

The coterminal for 86° will be however -360° + 86° = -274°

Summary:

The angle between 0° and 360° that is coterminal with -86° is 274°.