Trapezium arch

Weekly Problem 27 - 2007
Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?
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Trapezium Arch
Ten stones, of identical shape and size, are used to make an arch, as shown in the diagram. Each stone has a cross-section in the shape of a trapezium with equal sides. What is the size of the smallest angles of the trapezium?

 

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.