Question

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

Answer 1

Answer:

30°

Step-by-step 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° .