Question 1117558
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The sum of the interior angles of a pentagon is *[tex \LARGE (5\ -\ 2)(180)\ = 540] degrees.  Since it is a regular pentagon, the interior angles are all congruent, hence each interior angle measures 108 degrees.  Then 108 degrees is the measure of the apex angle of the two identical isosceles triangles.


Therefore *[tex \LARGE a\ =\ 108].  But the sum of the angles in any triangle is 180 degrees, so *[tex \LARGE a\ +\ 2b\ =\ 180].  From that we get *[tex \LARGE b\ =\ 36] after substituting for *[tex \LARGE a].


One vertex of the pentagon contains three angles, one from each of the three isosceles triangles, namely angles *[tex \LARGE b], *[tex \LARGE c], and *[tex \LARGE b].  We know that these three angles must add up to 108, and we know that two of them measure 36, so the third one, *[tex \LARGE c] must be 36 degrees as well.


Then, *[tex \LARGE c\ +\ 2d\ =\ 180].  You can calculate the size of *[tex \LARGE d] yourself.  Oh, and by the way, it is isosceles, not isoscales.  Yes, spelling counts.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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