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Answer:
-210° is a 2nd quadrant angle
-210 radians is a 3rd quadrant angle
-21° is a 4th quadrant angle
Step-by-step explanation:
If we assume you want the quadrant of the terminal ray of a standard-position angle whose measure is -210 degrees, then we can find the equivalent positive angle by adding 360°. The result is the coterminal angle of 150°. That lies between 90° and 180°, so is in the 2nd quadrant.
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The number given in this problem statement has no units attached. A "unitless" angle measure is a measure in <em>radians</em>. To normalize this angle of -210 radians, we can 68π radians to give a coterminal angle of about 3.628300 radians, or 207.9°. This angle lies between 180° and 270°, so is a 3rd quadrant angle.
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If the number given here is intended to be -21°, then it is measured 21° clockwise from the +x axis. That puts it in the 4th quadrant.
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<em>Additional comment</em>
We understand that sometimes the degree symbol does not get properly rendered when questions are copied to Brainly. We have seen it disappear (which we initially assumed was the case here), and we have seen it rendered as a zero (considered as an afterthought here). We also want to emphasize the fact that angles cannot be assumed to be in degrees, and that an angle in radians is equivalent to a pure number--one with no units at all. Hopefully we've covered enough bases that you can find the answer you want among those offered.
