OPQRSTUVWX is a regular decagon. A rotation of A degrees about U maps X to R. Given A < 180 degrees, find A.

Question

Thought it was 144 but it isn't.

Answer 1

Since the vertices are 36° apart, and X and R are 4 positions apart, it is indeed a central rotation of 144°.

However, we want to rotate about U, not the center of the decagon.

If you draw the figure, and if we call the center of the decagon A, then you can see that

<AUX = <AUR = 36°, so a rotation of 72° about U will move X to R.

Answer 2

Thanks!