Final answer:
The negative angle coterminal with 80 degrees is found by subtracting 360 degrees from 80, which gives -280 degrees. Therefore, the correct choice is option a) -280 degrees.
Step-by-step explanation:
To find the measure of a negative angle coterminal with 80 degrees, one must subtract 360 degrees from the positive angle until the result is negative. An angle coterminal with another angle has the same initial and terminal sides but may have a different number of complete rotations.
Starting with 80 degrees, we can calculate the negative coterminal angle by subtracting 360 degrees:
- 80 degrees - 360 degrees = -280 degrees
- 80 degrees - 2*360 degrees = -640 degrees (which is not one of the options)
Among the options provided, -280 degrees is the correct answer since it is the only one that results from subtracting 360 degrees from 80 degrees once.
Therefore, the correct option is a) -280 degrees.