Final answer:
The angle of rotation is 30 degrees.
Step-by-step explanation:
In order to find the angle of rotation, we can use the fact that the image of point M after a counterclockwise rotation can be obtained by rotating point M by the same angle in the clockwise direction. Since the points M and M' have rotated by the same angle, the line segment connecting them will form an angle with the positive x-axis. We can use the formula for the tangent of an angle to find the angle of rotation:
tan(θ) = (change in y-coordinate)/(change in x-coordinate)
Plugging in the values from the given points:
tan(θ) = (1 - (-1))/(2 - (-2)) = 2/4 = 1/2
Using a calculator or a table of trigonometric values, we can find that the angle whose tangent is 1/2 is 30 degrees. Therefore, the angle of rotation is 30 degrees.