To find an angle that is coterminal with a given angle (in this case, 110 degrees) within the range of 0 to 360 degrees, you can use the concept of adding or subtracting multiples of 360 degrees. Coterminal angles differ by full rotations (360 degrees), meaning that they point in the same direction on the unit circle.
Here’s how you can perform the calculations:
1. Start with your given angle: 110 degrees.
2. To find a positive coterminal angle, simply add 360 degrees:
110 + 360 = 470 degrees.
3. However, since 470 degrees is not within the range of 0 to 360 degrees, you can also find a negative coterminal angle by subtracting 360 degrees:
110 – 360 = -250 degrees.
4. To adjust this to find a coterminal angle within the specified range, you can add another 360 degrees to -250 degrees:
-250 + 360 = 110 degrees.
5. As you can see, since the original angle is already between 0 and 360 degrees, we can confirm that:
110 degrees is already coterminal within the range of 0 to 360 degrees.
Therefore, the measure of an angle between 0 degrees and 360 degrees that is coterminal with an angle of 110 degrees is 110 degrees.