Questions: Find the measure of the least positive angle that is coterminal with the angle given. Then find the measure of the negative angle that is nearest to and is coterminal with the angle given. -181° The positive angle is 179°. The negative angle is °.

Solution Steps

To find the least positive angle coterminal with a given angle, we add \(360^\circ\) to the angle until the result is positive. For the nearest negative coterminal angle, we subtract \(360^\circ\) from the angle until the result is negative.

To find the least positive angle coterminal with \(-181^\circ\), we add \(360^\circ\) to \(-181^\circ\) until the result is positive.

\[ -181^\circ + 360^\circ = 179^\circ \]

Thus, the least positive coterminal angle is \(179^\circ\).

To find the nearest negative angle coterminal with \(-181^\circ\), we subtract \(360^\circ\) from \(-181^\circ\) until the result is negative. Since \(-181^\circ\) is already negative, it is the nearest negative coterminal angle.

Final Answer