Answer:
210°
Explanation:
You want the angle in standard position to the point (-√3, -1).
Angle
The angle θ in standard position to a point (x, y) can be found from ...
tan(θ) = y/x
θ = arctan(y/x)
The arctangent function gives an angle between -90° and +90°, so will give the value of the reference angle in this case. To find the angle in quadrant III, we must add 180° to the reference angle.
θ = arctan(-1/-√3) + 180° = 210°
The angle shown is 210°.
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Additional comment
If you draw a vertical line from the point to the x-axis, you have a right triangle with side lengths 1 and √3. You know from your memory of special right triangles that this is a 30°-60°-90° triangle, whose smallest angle is 30°. This is the reference angle, so the angle of interest is 180° +30° = 210°.