# How do you determine the measure of an angle coterminal with the angle #400^circ#?

Coterminal of angle

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To determine the measure of an angle coterminal with the angle 400 degrees, you can add or subtract multiples of 360 degrees to the angle until you find an angle between 0 and 360 degrees. This is because angles that differ by a multiple of 360 degrees are coterminal, meaning they terminate in the same position when drawn in standard position.

For example, to find a positive coterminal angle, you can subtract 360 degrees from 400 degrees:

400 degrees - 360 degrees = 40 degrees

So, 40 degrees is a positive coterminal angle with 400 degrees.

To find a negative coterminal angle, you can add 360 degrees to 400 degrees:

400 degrees + 360 degrees = 760 degrees

Then, to find an angle between 0 and 360 degrees, you can subtract 360 degrees from 760 degrees:

760 degrees - 360 degrees = 400 degrees

Therefore, 400 degrees is a negative coterminal angle with 400 degrees.

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