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In the diagram below, points \(A\)\(E\), and \(F\) lie on the same line. If \(ABCDE\) is a regular pentagon, and \(\angle EFD=90^\circ\), then how many degrees are in the measure of \(\angle FDE\)?

 

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 Jun 30, 2023
 #1
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Angle FDE = 12 degrees.

 Jun 30, 2023
 #3
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Thanks, that's correct!

Guest Jul 5, 2023
 #2
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The formula for the sum of the internal angles of a regular polygon is

sum = (n – 2)(180) where n is the number of sides.   

 

For a pentagram, n is 5         so sum = (3)(180) = 540   

 

That's the sum, so an individual internal angle is a fifth of that, i.e., 108.  

 

That makes FED equal 180 – 108 = 72   

 

The sum of the angles of a triangle is 180, so FDE = 180 – (90 + 72) = 18  

 

Angle FDE is 18o   

 

had to edit because I misspelled polygon, grrr.  

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 Jun 30, 2023
edited by Bosco  Jun 30, 2023

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