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 \(360^{\circ}\), a straight - line (semicircle) is \(180^{\circ}\).

Step2: Estimate the angle

The angle from the positive \(x\) - axis, going clockwise, past \(180^{\circ}\). If we consider that the angle between each quadrant is \(90^{\circ}\), and the terminal side is about a third of the way into Quadrant III. \(180^{\circ}+ 60^{\circ}=240^{\circ}\) (since \(90\div1.5 = 60\), a rough estimate of the additional angle in Quadrant III).

Answer:

\(240^{\circ}\)