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The following diagonal is drawn in a regular heptagon, creating a pentagon and a quadrilateral. What is the measure of $x$, in degrees? Express your answer as a common fraction.

 

 

 Jun 27, 2018
 #1
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The sum of the interior  angles  of the heptagon will be  (7 - 2) * 180   = 900°

 

So...each  angle  will measure   (900/7)°

 

And the sum  of the interior angles in the quadrilateral  is  (4 - 2)* 180  =  360°

 

So...in the quadrilateral  we  have that the sum of the angles  = 360°

 

x + x  +  2 (900/7)  =  360      simplify

 

2x +  1800/ 7   =  360

 

2x  =   360  - 1800/7

 

2x  = [ 7 * 360   - 1800 ] / 7

 

2x  =  [720] / 7      divide both sides by 2

 

x  =  [ 720 ] / 14

 

x  = [360 / 7 ]°

 

 

cool cool cool

 Jun 27, 2018

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