Answer:
The angle of rotation at which point A′ coincides with point D is 144° counterclockwise or 216° clockwise.
Step-by-step explanation:
The given figure represents a regular pentagon. It means the central angle between two consecutive vertices is
[tex]\frac{360^{\circ} }{5}=72^{\circ}[/tex]
The vertex D is 2nd vertex from counterclockwise. So, the counterclockwise angle between A and D is
[tex]72^{\circ}\times 2=144^{\circ}[/tex]
The angle of rotation at which point A′ coincides with point D is 144° counterclockwise.
[tex]360^{\circ}-144^{\circ}=216^{\circ}[/tex]
The angle of rotation at which point A′ coincides with point D is 216° clockwise.
