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 />
  






 
  
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi><mo>+</mo><mn>2</mn><mo>&#x00D7;</mo><mn>120</mn><mo>+</mo><mn>2</mn><mo>&#x00D7;</mo><mn>108</mn><mo>=</mo><mn>5</mn><mo>&#x00D7;</mo><mn>108</mn><mo>=</mo><mn>540</mn></mrow></math>. hence
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>x</mi><mo>=</mo><mn>84</mn></mrow></math>.

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