Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 2 - Review Exercises - Page 117: 25


Number of sides: 8, 12, 20, 15, 10, 16, 180 Measure of each exterior $\angle$: 45$^{\circ}$, 30$^{\circ}$, 18$^{\circ}$, 24$^{\circ}$, 36$^{\circ}$, 23.5$^{\circ}$, 2$^{\circ}$ Measure of each interior $\angle$: 135$^{\circ}$, 150$^{\circ}$, 162$^{\circ}$, 156$^{\circ}$, 144$^{\circ}$, 157.5$^{\circ}$, 178$^{\circ}$ Number of diagonals: 20, 54, 170, 90, 35, 104, 15930

Work Step by Step

Use the information already in the table and the following formulas to solve the rest of the table: Measure of each interior angle (I) where n is the number of sides: I = ((n-2) $\times$ 180) $\div$ n Measure of each exterior angle (E) where (S) is the interior angle: E = 180 - I Number of diagonals (D) where n is the number of sides: D = (n(n-3)) $\div$ 2 Example: We are given 178$^{\circ}$ as the interior measure of one of the angles. First, we can find the exterior angle. 180$^{\circ}$ - 178$^{\circ}$ = 2$^{\circ}$. Next, we can find the number of sides. 178$^{\circ}$ = ((n-2) $\times$ 180) $\div$ n, which if we multiply both sides by n is equal to 178$^{\circ}$n = (n-2) $\times$ 180. 178 $\times$ 180 = (180 - 2) $\times$ 180, so there are 180 sides. Finally, we can find the number of diagonals. D = (180(180 - 3)) $\div$ 2 D = 15930
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