Question

draw an angle with the given measure in standard position.

1. 230°
2. 310°

find the reference angle.

1. -310°
2. -240°
3. 195°
4. 140°

Explanation:

Step1: Find reference angle for -310°

Add 360° to get positive coterminal angle: $-310° + 360° = 50°$. Since 50° is in Quadrant I, reference angle = 50°.

Step2: Find reference angle for -240°

Add 360° to get positive coterminal angle: $-240° + 360° = 120°$. 120° is in Quadrant II, so reference angle = $180° - 120° = 60°$.

Step3: Find reference angle for 195°

195° is in Quadrant III, so reference angle = $195° - 180° = 15°$.

Step4: Find reference angle for 140°

140° is in Quadrant II, so reference angle = $180° - 140° = 40°$.

Step5: Find reference angle for 230°

230° is in Quadrant III, so reference angle = $230° - 180° = 50°$.

Step6: Find reference angle for 310°

310° is in Quadrant IV, so reference angle = $360° - 310° = 50°$.

Answer:

-310°: 50°
-240°: 60°
195°: 15°
140°: 40°
230°: 50°
310°: 50°