Which of the following is a measure of an angle that is coterminal with a $95°$ angle?

• A. $185°$
• B. $5°$
• C. $455°$
• D. $275°$

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 360 degrees any number of times to an angle, the resulting angle is coterminal with the original.
2. Start with the given angle, which is 95 degrees. To find coterminal angles, add or subtract multiples of 360 degrees: \$95^\circ + 360^\circ \times k\(, where \)k$ is any integer (positive, negative, or zero).
3. Check each given option by subtracting 95 degrees and see if the difference is a multiple of 360 degrees. For example, for 185 degrees, calculate \$185^\circ - 95^\circ = 90^\circ$, which is not a multiple of 360, so 185 degrees is not coterminal.
4. Repeat this for 5 degrees: \$5^\circ - 95^\circ = -90^\circ$, which is also not a multiple of 360, so 5 degrees is not coterminal.
5. For 455 degrees: \$455^\circ - 95^\circ = 360^\circ$, which is exactly one full rotation, so 455 degrees is coterminal with 95 degrees. Similarly, check 275 degrees to confirm it is not coterminal.