c) 180 degrees
If you have a parallelogram and recall that a parallelogram is every quadrilateral having parallel both pairs of opposite sides, so if you rotate this shape 180 degrees, then image will coincide with its preimage. To do this, you need to consider each point as [tex]P(x,y)[/tex] and apply the rule:
[tex](x,y)\rightarrow(-x,-y)[/tex]
This rule allows us to rotate this point by 180° around the origin. Suppose you have a parallelogram build up by these coordinates:
[tex]P_{1}(a,b) \\ \\ P_{2}(-a,b) \\ \\ P_{3}(a,-b) \\ \\ P_{4}(-a,-b)[/tex]
By applying the rule we have:
[tex]P'_{1}(-a,-b) \\ \\ P'_{2}(a,-b) \\ \\ P'_{3}(-a,b) \\ \\ P'_{4}(a,b)[/tex]
So we can form the same figure by the resulting points and this is true because:
[tex]P_{1}=P'_{4} \\ \\ P_{2}=P'_{3} \\ \\ P_{3}=P'_{2} \\ \\ P_{4}=P'_{1}[/tex]
