Answer:
A. 72°
D. 144°
E. 216°
Explanation:
are you tempted to calculate the internal angles ?
that is, I guess, the trap set by your teacher here, and it would be the wrong approach.
nevertheless, quickly just as a reminder :
the sum of all internal angles in a polygon is
(n - 2)×180°
n being the number of sides.
in our case that is
(5 - 2)×180 = 3×180 = 540°
so, each internal angle is 540/5 = 108°.
but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.
we are running each vertex along a circle arc. the center of that circle being P.
after every 1/5 of the circle arc there is a vertex of the pentagon.
and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.
so, instead of a full circle rotation we need only 1/5 of that :
360 / 5 = 72°
and with every additional 1/5 of the circle arc (or 72°) we get it again.
that means at
72°
144°
216°
288°
360°
the pentagon carries onto itself.
therefore, A, D and E are correct.