Question

The angle of rotation at which point A′ coincides with point D is_
°.

Answer 1

I think the answer is 144.

Answer 2

The angle of rotation at which point A′ coincides with point D is 144° counterclockwise or 216° clockwise.

Explanation:

The given figure represents a regular pentagon. It means the central angle between two consecutive vertices is

`(360^(\circ) )/(5)=72^(\circ)`

The vertex D is 2nd vertex from counterclockwise. So, the counterclockwise angle between A and D is

`72^(\circ)* 2=144^(\circ)`

The angle of rotation at which point A′ coincides with point D is 144° counterclockwise.

`360^(\circ)-144^(\circ)=216^(\circ)`

The angle of rotation at which point A′ coincides with point D is 216° clockwise.