Which of the following pairs of angles have the same reference angle?

• A. $90°$ and $270°$
• B. $45°$ and $135°$
• C. $60°$ and $120°$
• D. $30°$ and $150°$

Answer: (D)

Verified step by step guidance

1. Recall that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis. It is always between 0° and 90°.
2. For angles in the first quadrant (0° to 90°), the reference angle is the angle itself.
3. For angles in the second quadrant (90° to 180°), the reference angle is calculated as \$180^\circ - \theta\(, where \)\theta$ is the given angle.
4. Calculate the reference angles for each pair: for example, for 30° and 150°, the reference angle for 30° is 30°, and for 150°, it is \$180^\circ - 150^\circ = 30^\circ$.
5. Compare the reference angles of each pair to determine which pairs have the same reference angle.