In this exercise you will verify some of the properties of
Chapter 9, Problem 45(choose chapter or problem)
In this exercise you will verify some of the properties of the pentagram star shown in Figure A. Figure B shows how the pentagram is constructed. We start with a regular pentagon ABCDE inscribed in a circle with center O. Drawing the diagonals of the pentagon then yields the pentagram star. As indicated in Figure B, the five intersection points (S, T, U, V, and W) of the diagonals form the vertices of a second, smaller regular pentagon. In this exercise you can assume the following facts (which can be established using elementary geometry): Each of the five triangles AUV, BVW, CWS, DST, and ETU is isosceles, with angles of 72, 72, and 36. In a regular pentagon, each interior angle is 108. (For example, in the large regular pentagon, AED 108, and in the small pentagon, VUT 108.)
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