ABCDEFGHIJ is a regular decagon. The rotation centered at G with an angle of alpha takes I to E. Given that alpha is less than 180 degrees, find alpha.

A regular decagon is rotationally symmetrical by 360/10 = 36 degrees.

To take I to E, that rotation needs to be done 4 times, so alpha is equal to \(4(36)=\boxed{144}\)