Question

Which expression can be used to determine the reference angle for an angle, x, measuring 150°?

Answer 1

30°

Explanation:

Angles and Quadrants:

• 0° to 90° -- Quadrant 1
• 90° to 180° -- Quadrant 2
• 180° to 270° -- Quadrant 3
• 270° to 360° -- Quadrant 4

Formula for Reference Angle in each Quadrant:

`\theta` is the angle given

• Quadrant 1 -- Reference Angle =
  `\theta`
• Quadrant 2 -- Reference Angle =
  `180-\theta`
• Quadrant 3 -- Reference Angle =
  `\theta - 180`
• Quadrant 4 -- Refence Angle =
  `360-\theta`

Angle given is 150°, which according to first table, falls in Quadrant 2.

According to second table, the reference angle is found by subtracting 150° from 180°.

Reference Angle = 180° - 150° = 30°

Answer 2

To find the reference angle measuring x for angle in Quadrant II the formula is:
180° - x = 180° - 150° = 30°
Answer: the reference angle is 30° .