We have been given a regular pentagon and we are asked to find all the correct options about measurements at which the polygon has rotational symmetry.
Since we know that measure of central angle of a pentagon is 360 degrees. To find rotational symmetry of our pentagon we will divide 360 by 5 (number of sides of our polygon).
[tex]\text{Rotational symmetry of a pentagon}=\frac{360}{5} =72[/tex]
A rotation of 72 degree will map each vertices of pentagon to its consecutive vertices.
Any multiple of 72 degree will also map each vertex of pentagon to its next vertex.
Let us see which of the given options are multiples of 72.
[tex]72\cdot 1=72[/tex]
[tex]72\cdot 2=144[/tex]
Therefore, 72° and 144° are the angle measurements at which our pentagon will have rotational symmetry.
