Find the angle of least positive measure (in degrees, not equal to the given measure) that is coterminal with the given angle.
$$-{122}^{\circ }{50}^{\prime }$$
The angle of least positive measure coterminal with $-{122}^{\circ }{50}^{\prime }$ is

Step 1 ：Convert the given angle to decimal form. The given angle is -122 degrees and 50 minutes. We know that 1 degree is equal to 60 minutes, so we can convert 50 minutes to degrees by dividing by 60. This gives us $-122+\frac{50}{60}=-121.83333333333333$ degrees.

Step 2 ：To find the coterminal angle, we need to add or subtract multiples of 360 degrees until we get an angle in the desired range. In this case, we want the smallest positive angle coterminal with the given angle. So, we add 360 degrees to the given angle: $-121.83333333333333+360=238.16666666666669$ degrees.

Step 3 ：Therefore, the angle of least positive measure coterminal with $-{122}^{\circ }{50}^{\prime }$ is $\boxed{{\displaystyle {238.17}^{\circ }}}$.