Which of the following angle measures in degrees are coterminal with $45°$ in standard position?

• A. $225°$
• B. $-315°$
• C. $405°$
• D. $135°$

Answer: (C)

Verified step by step guidance

1. Recall that two angles are coterminal if they differ by a full rotation, which is 360 degrees. This means if you add or subtract multiples of 360° to an angle, you get angles coterminal with it.
2. Start with the given angle, 45°, and find angles coterminal by adding 360°: \$45^\circ + 360^\circ = 405^\circ$.
3. Next, find coterminal angles by subtracting 360°: \$45^\circ - 360^\circ = -315^\circ$.
4. Check the other given angles to see if they can be expressed as \$45^\circ \pm 360^\circ \times k\( where \)k\( is an integer. For example, 225° is not coterminal because \)225 - 45 = 180$, which is not a multiple of 360.
5. Conclude that the angles coterminal with 45° from the given options are those that can be written as \$45^\circ \pm 360^\circ\(, specifically \)-315^\circ\( and \)405^\circ$.