Question

which expression can be used to determine the reference angle for an angle, x, measuring 150°?
○ 180° - x
○ x - 180°
○ 360° - x
○ x - 360°

Explanation:

Step1: Recall reference angle rules

Reference angle for an angle in the second quadrant (90° < x < 180°) is \( 180^\circ - x \).

Step2: Check angle's quadrant

\( 150^\circ \) is in the second quadrant (90° < 150° < 180°).

Step3: Apply the rule

Using the rule for second - quadrant angles, the reference angle is \( 180^\circ - x \) (substituting \( x = 150^\circ \), we get \( 180^\circ-150^\circ = 30^\circ \), which is the reference angle). The other options: \( x - 180^\circ=150 - 180=- 30^\circ \) (magnitude but sign is wrong, and not the formula for second - quadrant), \( 360^\circ - x = 360 - 150 = 210^\circ \) (for fourth - quadrant), \( x - 360^\circ=150 - 360=-210^\circ \) (not relevant for second - quadrant).

Answer:

\( 180^{\circ}-x \) (the first option: \( 180^{\circ}-x \))