Solve this problem.
the sum of the interior angles of a pentagon is 540 degrees. the pentagon in washington, d. c, is named for its unusual shape, a regular pentagon. what is the measure of each angle of the pentagon?

468

step-by-step explanation:

40 minutes

step-by-step explanation:

add the time and multiply by 2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4