The angles at a point add up to 360°.
Draw the Pentagon and join each vertex to point X (the center of the Pentagon).
This gives us 5 isosceles triangles. Since the polygon is regular, the angles at the center (∅) are equal.
Ф=360÷5=72°
We can now get the angle of rotation by either moving clockwise or anticlockwise.
This means we are going to have 2 answers.
1. The angle of rotation in clockwise direction = 72°×2=144°
2. The angle rotation in anticlockwise direction = 72°×3=216°