Regular pentagon ABCDE rotates counterclockwise about its center to yield pentagon A'B'C'D'E'. At which angle of rotation does A' coincide with D?

A.320
B.288
C.216
D.144
E.72

Question

Regular pentagon ABCDE rotates counterclockwise about its center to yield pentagon A'B'C'D'E'. At which angle of rotation does A' coincide with D?

A.320
B.288
C.216
D.144
E.72

anonymous · Answer

Try drawing it out:

|dw:1403655354082:dw|

if a circle is 360 degrees or 2pi radians, then each of the points of a regular pentagon would account for one fifth (1/5) of that total circle. so to rotate the pentagon to D, you need to rotate the starting end point A through B, C and then to D. Thats 3 sections. So what angle would that be?

anonymous · Answer

im not sure never did a problem like this before

anonymous · Answer

alright, well can you see that rotating the pentagon all the way around would be 360 degrees as it would go full circle. I'll try and draw some examples out for you:

|dw:1403655591006:dw|

see that rotating the pentagon from one letter to another is a rotation of 360/5 = 72 degrees or 2/5 pi radians:

|dw:1403655812252:dw|