geometry - help study for final (5-pointed star)

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missa0312

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Mar 5, 2006
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Show that for any 5-pointed star, the measure of angle A + the measure of angle B + the measure of angle C + the measure of angle D + the measure of angle E = 180. (The point A,B,C,D, and E are the the angles at the 5 points of the star.)
 
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What you are really trying to prove is that angle A, B, C, D, and E are all 36 degrees, because there are five points on the star and 180/5 = 36.

Ok you have your star, notice that there is a regular pentagon in the center. The sum of the angles of a pentagon always add up to 540 degrees. So therefore, each individual angle in that pentagon is 108 degrees.
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Looking at this portion of the star you can see that angle Y and the angle of the pentagon is supplementary, and thats basically all you need to prove that angle X = 36.
 
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