Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 333: 24

Answer

(a) $225^{\circ}$ (b) $300^{\circ}$

Work Step by Step

(a) We can find the number of vertices of the polygon: $45^{\circ} = \frac{360^{\circ}}{n}$ $n = \frac{360^{\circ}}{45^{\circ}}$ $n = 8$ We can find the interior angle of this polygon: $\frac{(n-2)(180^{\circ})}{n} = \frac{(8-2)(180^{\circ})}{8} = 135^{\circ}$ We can find the exterior angle of this polygon: $360^{\circ} - 135^{\circ} = 225^{\circ}$ (b) We can find the number of vertices of the polygon: $120^{\circ} = \frac{360^{\circ}}{n}$ $n = \frac{360^{\circ}}{120^{\circ}}$ $n = 3$ We can find the interior angle of this polygon: $\frac{(n-2)(180^{\circ})}{n} = \frac{(3-2)(180^{\circ})}{3} = 60^{\circ}$ We can find the exterior angle of this polygon: $360^{\circ} - 60^{\circ} = 300^{\circ}$
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