Which of the following pairs of angles are coterminal angles in standard position?

• A. $45°$ and $135°$
• B. $60°$ and $120°$
• C. $30°$ and $390°$
• D. $90°$ and $270°$

Answer: (C)

Verified step by step guidance

1. Recall that coterminal angles are angles in standard position that share the same terminal side. This means their measures differ by a full rotation, which is 360 degrees.
2. To check if two angles \( \theta_1 \) and \( \theta_2 \) are coterminal, calculate the difference \( |\theta_1 - \theta_2| \) and see if it is a multiple of 360 degrees.
3. For example, for the pair 30° and 390°, compute the difference: \( |30 - 390| = 360 \) degrees, which is exactly one full rotation, so these angles are coterminal.
4. For other pairs, such as 45° and 135°, calculate \( |45 - 135| = 90 \) degrees, which is not a multiple of 360, so they are not coterminal.
5. Apply this method to each pair to determine which pairs are coterminal by checking if their difference is \( 360k \) degrees, where \( k \) is an integer.