Question

estimate the given rotation within 10 degrees:

Explanation:

Step1: Analyze the position of the terminal side

The terminal side is in the second quadrant. A full - circle is \(360^{\circ}\), a half - circle is \(180^{\circ}\), and a right - angle is \(90^{\circ}\).

Step2: Estimate the rotation

The angle is more than \(90^{\circ}\) (since it's past the positive \(y\) - axis) and less than \(180^{\circ}\). By visual inspection, it is approximately \(150^{\circ}\) (because \(180 - 30=150\), and it looks about \(30^{\circ}\) away from the negative \(x\) - axis).

Answer:

\(150^{\circ}\)