Coterminal angles are angles that have the same terminal sides in standard position.
Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.
Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].
For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],
We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.
This means that
[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]
Hence the correct and answer is D
