Question

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

Explanation:

Step1: Recall basic angle measures

A right - angle is \(90^{\circ}\), and a straight - angle is \(180^{\circ}\).

Step2: Estimate the angle

The angle is in the second quadrant. The angle from the positive \(x\) - axis to the negative \(x\) - axis is \(180^{\circ}\). The given angle is less than \(180^{\circ}\) and more than \(90^{\circ}\). By visual inspection (comparing to known angles like \(90^{\circ}\), \(120^{\circ}\), \(150^{\circ}\)), we can estimate. If we consider that a \(120^{\circ}\) angle (\(90^{\circ}+ 30^{\circ}\)) and a \(150^{\circ}\) angle (\(90^{\circ}+60^{\circ}\)), the angle in the figure is closer to \(150^{\circ}\) (since \(150^{\circ}=180 - 30\) and it seems that the non - rotated part from the negative \(x\) - axis is about \(30^{\circ}\)).

Answer:

\(150\)