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 \(\angle FDE\)?

Keihaku Jun 30, 2023

#2**0 **

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 18 ^{o}**

had to edit because I misspelled polygon, grrr.

_{.}

Bosco Jun 30, 2023