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Two Answers:  

Explanation:

To find a coterminal angle, we can either add or subtract 360 from the given angle.

Adding on 360 gets us -135+360 = 225

Adding another copy of 360 gets us 225+360 = 585, which isn't on the list. It exceeds the largest value 495, so we can stop adding on copies of 360.

Let's go back to -135 and subtract 360 to see what we get

-135 - 360 = -495

Repeat again to get

-495-360 = -855

but that's not on the list. We can stop here because -495 is the smallest item on this list.

The reason why we add/subtract 360 is because we're rotating a full 360 degrees to get to another coterminal angle. The angle -135 is coterminal to 225 degrees as they both point directly in the southwest direction.

As another example, the angle 90 degrees and 90+360 = 450 degrees are coterminal since they both point directly north.

step-by-step explanation: