Question

estimate the given rotation within 10 degrees:
answer attempt 1 out of 3
estimated angle: □°

Explanation:

Step1: Analyze the position of the terminal side

The terminal side is in Quadrant III. A full - circle rotation is \(360^{\circ}\), and a straight - line (semicircle) is \(180^{\circ}\).

Step2: Estimate the angle

The angle is more than \(180^{\circ}\). If we consider that from the negative \(x\) - axis (which is \(180^{\circ}\)), the terminal side is about \(60^{\circ}\) past the negative \(x\) - axis in the clockwise (negative) direction. So the angle is \(180 + 60=240^{\circ}\) (since \(180^{\circ}+60^{\circ}\) gives a reasonable estimate within \(10^{\circ}\) for the position of the terminal side in Quadrant III).

Answer:

\(240^{\circ}\)