Final answer:
The positive co-terminal angle to 310 degrees that is between 360 and 720 degrees is 670 degrees, which is found by adding 360 degrees to the original angle.
Step-by-step explanation:
To find a positive co-terminal angle to 310 degrees that lies between 360 and 720 degrees, we need to add or subtract multiples of 360 degrees to the given angle until we find an angle within the desired range. Since we are looking for a positive angle, we will add 360 degrees to 310 degrees:
- Add 360 degrees to 310 degrees: 310 + 360 = 670 degrees.
The angle 670 degrees is a positive co-terminal angle to 310 degrees and falls within the requested range of between 360 and 720 degrees.