# Science:Math Exam Resources/Courses/MATH152/April 2022/Question A18/Solution 1

Let be the line that makes an angle of with the positive -axis, and be the line that makes an angle of with the positive -axis. We sketch the sequence of reflections below, keeping the original orientation of the axes in the background, labelled as , . In the sketch, the image of the -, -axes after is labelled as , . The reflection is then applied to the -, -axes, resulting in the -, -axes.

After the reflection about , we now look at the angle between the axes and , this is (shown in purple). The - and -axes are now off from their original orientation (taking counterclockwise rotation to be positive).