Teaser 1885: Sacred sign

From The Sunday Times, 1st November 1998 [link]

The “Sacred Sign of Solomon” consists of a pentagon whose vertices lie on a circle, roughly as shown:

Starting at one of the angles and going round the circle the number of degrees in the five angles of the large pentagon form an arithmetic progression; i.e., the increase from the first to the second equals the increase from the second to the third, etc.

As you can see, the diagonals form a small inner pentagon and in the case of the sacred sign one of its angles is a right angle.

What are the five angles of the larger pentagon?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book.

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