Question

Regular decagon ABCDEFGHIJ rotates 360 counterclockwise about it's center. At which angle of rotation does A' (the image of A) coincide with D?

Answer 1

For the answer to the question above,
ABCDEFGHIJ is a regular decagon.
If sides are extended to meet at K,
find the measure of <K.
The total degree measure in a decagon is 180(8)
since a decagon can be broken up into 8 triangles.
In a regular decagon,
each angle has the same measure: 180(8)/10 = 18(8) = 144.
The supplementary angle, 36, is, therefore, the angle between the side BC
and (each of) the two extended sides AB, CD outside of the decagon.
The remaining angle, K, of the triangle thus formed is 180-2(36) = 180 - 72 = 108