Question

estimate the given rotation within 10 degrees:

Explanation:

Step1: Analyze the position of the terminal side

The terminal side is in Quadrant III.

Step2: Estimate the angle

A full - circle is \(360^{\circ}\). The positive \(x\) - axis to the negative \(x\) - axis is \(180^{\circ}\), and the negative \(x\) - axis to the negative \(y\) - axis is another \(90^{\circ}\). The given rotation is more than \(180^{\circ}\). If we assume a rough estimate, since it is in the lower - left part (Quadrant III) and not too close to the negative \(y\) - axis. A \(210^{\circ}\) rotation would point to the negative \(x\) - axis direction, and a \(270^{\circ}\) rotation points to the negative \(y\) - axis. The given rotation seems to be about \(220^{\circ}\) (since \(180 + 40=220\), and it is a rough estimate within \(10^{\circ}\) as the problem asks.

Answer:

\(220^{\circ}\)