Sure! Let's determine which angle is coterminal with 150°. Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. To find coterminal angles, you can add or subtract multiples of 360° to the given angle.
Here are the steps to determine coterminal angles with 150°:
1. Begin with the given angle, which is 150°.
2. Add and subtract multiples of 360° to find additional angles that are coterminal with 150°.
- 150° + 360° = 510°
- 150° + 2(360°) = 870°
- 150° - 360° = -210°
- 150° - 2(360°) = -570°
Next, we will match these calculated coterminal angles with the provided choices:
A. 500°
B. -150°
C. 510°
D. 330°
Comparing each choice with our calculated values, we see that:
- 500° is not in our calculated coterminal angles.
- -150° is not in our calculated coterminal angles.
- 510° matches one of our calculated coterminal angles (150° + 360°).
- 330° is not in our calculated coterminal angles.
Thus, the angle that is coterminal with 150° is:
C. 510°
