Question

estimate the given rotation within 10 degrees:

Explanation:

Step1: Analyze the position

The rotation is from the positive \(x -\)axis to a point in Quadrant II.

Step2: Estimate the angle

A full - circle is \(360^{\circ}\), a half - circle is \(180^{\circ}\). The angle between the positive \(x -\)axis and the negative \(x -\)axis is \(180^{\circ}\). The given rotation is less than \(180^{\circ}\). If we consider that the line is closer to the negative \(x -\)axis. A quarter - circle is \(90^{\circ}\), and the angle between the positive \(x -\)axis and the line in the second quadrant. If we assume that the line divides the second quadrant in a way. Since \(180^{\circ}- 150^{\circ}=30^{\circ}\) (distance from negative \(x -\)axis), and \(180^{\circ}-160^{\circ} = 20^{\circ}\), \(180^{\circ}-140^{\circ}=40^{\circ}\). A reasonable estimate within \(10^{\circ}\) is \(160^{\circ}\) (because if we consider that the angle from the positive \(x -\)axis, and we know that \(150^{\circ}<\theta<170^{\circ}\))

Answer:

\(160^{\circ}\)