Question

find the angle of rotation and direction (clockwise or counterclockwise) that maps a to a.

55°
degrees

Explanation:

Step1: Calculate the angle of rotation

The total angle around a point is \(360^{\circ}\). If we assume the non - rotated position and the two rotated positions, and we know one of the angles between the non - rotated and a rotated position is \(55^{\circ}\).
The angle of rotation from \(A\) to \(A''\) is \(180^{\circ}- 55^{\circ}=125^{\circ}\) (using the property of angles formed by two intersecting lines and the concept of rotation).

Step2: Determine the direction

By observing the orientation of the figure (assuming the standard position of angles in a plane), the direction of rotation from \(A\) to \(A''\) is counterclockwise.

Answer:

125 degrees, counterclockwise