Which expression can be used to determine the reference angle for an angle $\theta$ in standard position if $\theta >180°$ but $\theta <360°$?

• A. $360°-\theta$
• B. $180°-\theta$
• C. $\theta -180°$
• D. $\theta$

Answer: (A)

Verified step by step guidance

1. Understand that the reference angle is the acute angle formed between the terminal side of the given angle \( \theta \) and the x-axis.
2. Since \( \theta \) is in standard position and lies between 180° and 360°, it is located in either the third or fourth quadrant.
3. For angles in the third quadrant (180° to 270°), the reference angle is found by subtracting 180° from \( \theta \), i.e., \( \theta - 180^\circ \).
4. For angles in the fourth quadrant (270° to 360°), the reference angle is found by subtracting \( \theta \) from 360°, i.e., \( 360^\circ - \theta \).
5. Since the problem states \( 180^\circ < \theta < 360^\circ \) without specifying the quadrant, the general expression to find the reference angle for angles in this range is \( 360^\circ - \theta \).