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The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral.

 

 

Another diagonal is drawn.

 

 

What is the measure of x, in degrees? Express your answer as a common fraction.

 Dec 3, 2020
 #1
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If the heptagon were inscribed in a circle, each  side  of of the heptagon  would span an  arc of  ( 360 / 7)°

 

The diagonals would form chords within this circle

 

So....using the angle of intersecting chords theorem  we have that

 

x  =  (1/2)  [ 2 (360/7) +  3(360/7)  ]    =  (1/2) [ 5 (360/7 ] =    [900/7]°     (  ≈  128.57°  )

 

cool cool cool

 Dec 3, 2020

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