document.write( "Question 390241: A “five-pointed star” can be constructed by taking a regular pentagon and drawing
\n" ); document.write( "straight lines from the first vertex to the third, the third to the fifth, the fifth to the second, and so on. Prove that the sum of the angles of the five vertices of the star is 180 degrees.
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Algebra.Com's Answer #276670 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Draw the circumscribed circle and radii to the vertices:\r\n" );
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document.write( "The two angles marked 72° are 72° each because they are one-fifth \r\n" );
document.write( "of 360°.  \r\n" );
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document.write( "The two angles marked 18° are 18° because they are base angles of\r\n" );
document.write( "an isosceles triangle whose vertex angle is twice 72° or 144° and\r\n" );
document.write( "180°-144° = 36° and since the base angles of an isosceles triangle\r\n" );
document.write( "are congruent, each has measure of half of 36° or 18°.\r\n" );
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document.write( "Similarly, you can show that these angles are as marked below, too:\r\n" );
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document.write( "So therefore one of the points of the star makes an angle\r\n" );
document.write( "of 36° since it is twice 18°, as indicated below:\r\n" );
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document.write( "By the same reasoning, each of the points of the star makes\r\n" );
document.write( "an angle of 36°, so therefore the sum of the angles made at\r\n" );
document.write( "all five points of the star is 5×36° = 180°.\r\n" );
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document.write( "This is just an outline of how to prove it.  You have to write it \r\n" );
document.write( "up as a two-column proof yourself.  You'll have to label some of\r\n" );
document.write( "the points with letters so you can talk about triangles such as\r\n" );
document.write( "triangle ABC, and angles PQR, etc., or whatever lettering system\r\n" );
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document.write( "Edwin
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