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

• A. $\theta =45°$ and $\theta =135°$
• B. $\theta =60°$ and $\theta =120°$
• C. $\theta =30°$ and $\theta =90°$
• D. $\theta =0°$ and $\theta =180°$

Answer: (A)

Verified step by step guidance

1. Recall that the reference angle for an angle \( \theta \) in standard position is the acute angle formed between the terminal side of \( \theta \) and the x-axis.
2. For angles in the first quadrant (0° to 90°), the reference angle is the angle itself, so \( \text{reference angle} = \theta \).
3. For angles in the second quadrant (90° to 180°), the reference angle is calculated as \( 180^\circ - \theta \).
4. Calculate the reference angles for each pair given: for example, for \( 45^\circ \) and \( 135^\circ \), the reference angles are \( 45^\circ \) and \( 180^\circ - 135^\circ = 45^\circ \), respectively.
5. Compare the reference angles of each pair to determine which pairs have the same reference angle.