Question

reference angle of 220 degree 180 140 360 50

Explanation:

Step1: Determine the quadrant of 220°

220° is between 180° and 270°, so it's in the third quadrant.

Step2: Calculate the reference angle

For an angle \( \theta \) in the third quadrant (\( 180^\circ < \theta < 270^\circ \)), the reference angle is \( \theta - 180^\circ \).
So for \( \theta = 220^\circ \), the reference angle is \( 220^\circ - 180^\circ = 40^\circ \)? Wait, wait, the options given are 180, 140, 360, 50. Wait, maybe I made a mistake. Wait, no, wait the options seem wrong? Wait no, wait maybe the question is miswritten? Wait no, wait the angle is 220 degrees. Wait, reference angle formula: in third quadrant, reference angle is \( \theta - 180^\circ \). So 220 - 180 = 40. But 40 is not an option. Wait, maybe the angle is 230? No, the problem says 220. Wait, maybe the options are wrong, but among the given options, let's check again. Wait, maybe I miscalculated. Wait, 220 - 180 = 40. But the options are 180,140,360,50. Wait, maybe the question is about something else? Wait no, reference angle. Wait, maybe the angle is 220 radians? No, it's degrees. Wait, maybe the options are incorrect, but perhaps there's a typo. Wait, maybe the angle is 230? 230 - 180 = 50. Oh! Maybe the angle is 230, but the problem says 220. Wait, but the options have 50. So maybe a typo, and the intended angle is 230, so reference angle is 50. So the answer would be 50.

Answer:

50 (assuming a possible typo in the angle, as 220 - 180 = 40 which is not an option, but 230 - 180 = 50 which is an option)