# SOLUTION: A “five-pointed star” can be constructed by taking a regular pentagon and drawing straight lines from the first vertex to the third, the third to the fifth, the fifth to the secon

Algebra ->  Algebra  -> Polygons -> SOLUTION: A “five-pointed star” can be constructed by taking a regular pentagon and drawing straight lines from the first vertex to the third, the third to the fifth, the fifth to the secon      Log On

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 Geometry: Polygons Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Polygons Question 390241: A “five-pointed star” can be constructed by taking a regular pentagon and drawing 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. Answer by Edwin McCravy(8889)   (Show Source): You can put this solution on YOUR website!``` Draw the circumscribed circle and radii to the vertices: The two angles marked 72° are 72° each because they are one-fifth of 360°. The two angles marked 18° are 18° because they are base angles of an isosceles triangle whose vertex angle is twice 72° or 144° and 180°-144° = 36° and since the base angles of an isosceles triangle are congruent, each has measure of half of 36° or 18°. Similarly, you can show that these angles are as marked below, too: So therefore one of the points of the star makes an angle of 36° since it is twice 18°, as indicated below: By the same reasoning, each of the points of the star makes an angle of 36°, so therefore the sum of the angles made at all five points of the star is 5×36° = 180°. This is just an outline of how to prove it. You have to write it up as a two-column proof yourself. You'll have to label some of the points with letters so you can talk about triangles such as triangle ABC, and angles PQR, etc., or whatever lettering system you want to use. Edwin```