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find one angle with positive measure and one angle with negative measure coterminal with -310°
First we draw the picture of -310°. We start at
the right side of the x-axis, then swing downward
and around in the CLOCKWISE direction through 310°,
as shown by the black CLOCKWISE arc below:
Notice that 310° just lacks 50° being 360°, since
360°-310° = 50° so the positive angle 50° measured in the
COUNTER-CLOCKWISE direction is coterminal with -310°, as
shown by the COUNTER-CLOCKWISE red arc below:
So a positive angle coterminal with -310° is 50°.
To find a negative angle coterminal with -310, we
just need to go around 360° more in the CLOCKWISE
direction like this:
which means we just add -360° to -310° and get -670°.
So a negative angle coterminal with -310° is -670°.