Question

estimate the given rotation within 10 degrees: answer attempt 1 out of 3 estimated angle: ^{circ }

Explanation:

Step1: Analyze the position of the angle

The angle is in the third - quadrant. A full - circle is \(360^{\circ}\), a straight - line (semicircle) is \(180^{\circ}\).

Step2: Estimate the angle

We know that \(180^{\circ}\) is a straight - line. The given angle is more than \(180^{\circ}\). If we assume that the angle from the negative \(x\) - axis to the terminal side of the angle is approximately \(30^{\circ}\) (by visual inspection). Then the angle \(\theta\) is \(180^{\circ}+ 30^{\circ}=210^{\circ}\)

Answer:

\(210^{\circ}\)