I started a new section in our geometry book with my older son today and spent the morning talking about sums of interior and exterior angles. He had an appointment for an orthopedist to look at his broken hand from a sledding accident, so I wanted to keep things fairly light for the rest of the day. This problem I saw on twitter hit the spot exactly:
My son’s initial reaction was great – make everything totally symmetric and see what happens. Love it:
But, that doesn’t solve the problem – we don’t know that all of the sides of that interior pentagon are equal. What next?
It turned out that this was a nice example of how simplifying a problem can help you find a solution since basically the same solution to the simple problem works in general. He had a little hiccup at the end with the final subtraction, but all in all a nice solution to a neat exercise. Love it when I see great problems on Twitter 🙂
Mike's Math Page 
This is one of those problems in which a pencil is more use than a muse! Think exterior angles of a triangle and a sliding pencil.