+656 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 \(\angle FDE\)?
+802
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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