Each interior angle of a regular pentagon is 108 degrees, whilst
  each interior angle of a regular hexagon is 120 degrees. The
  non-regular pentagon in the centre of the diagram contains two
  angles which are interior angles of the regular hexagon, two
  angles which are interior angles of the regular hpentagon and a
  fifth angle, the one marked x. So:<br />
  



 
  <i>x</i>+2&#x00D7;120+2&#x00D7;108 =  5&#x00D7;108 = 540. hence<i>x</i>=84.



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