Enigma 1752: Pentagon of squares
From New Scientist #2920, 8th June 2013 [link]
I have drawn a circle, marked five points around its circumference, and joined each to the next by a straight line in order to make a pentagon. It turns out that the centre of the circle is outside this pentagon. I have then measured, in degrees, the five interior angles of the pentagon. The five numbers are all different and all but the smallest are perfect squares.
What is the smallest angle and what are the angles on either side of the smallest one?