Question

find the measure of the reference angle for a 595° angle.

Explanation:

Step1: Reduce the angle by 360°

To find the coterminal angle within 0° to 360°, subtract 360° from 595°:
\( 595^\circ - 360^\circ = 235^\circ \)

Step2: Determine the quadrant of 235°

235° lies in the third quadrant (180° < 235° < 270°).

Step3: Calculate the reference angle

For an angle \( \theta \) in the third quadrant, the reference angle is \( \theta - 180^\circ \):
\( 235^\circ - 180^\circ = 55^\circ \)

Answer:

\( 55 \)