cyclic pentagon

Here's a nice little puzzle that was in the new scientist recently.

I chose 5 points, on the perimeter of a circle, all on one side of a diameter.

I then joined those 5 points to form a convex pentagon.

Measuring the internal angles of the pentagon, in degrees, I found that all except the smallest angle were a square whole number of degrees.

What is the smallest angle and the two angles adjacent to it?