## Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

# Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 333: 23

#### Answer

(a) $210^{\circ}$ (b) $220^{\circ}$

#### Work Step by Step

(a) We can find the number of vertices of the polygon: $30^{\circ} = \frac{360^{\circ}}{n}$ $n = \frac{360^{\circ}}{30^{\circ}}$ $n = 12$ We can find the interior angle of this polygon: $\frac{(n-2)(180^{\circ})}{n} = \frac{(12-2)(180^{\circ})}{12} = 150^{\circ}$ We can find the exterior angle of this polygon: $360^{\circ} - 150^{\circ} = 210^{\circ}$ (b) We can find the number of vertices of the polygon: $40^{\circ} = \frac{360^{\circ}}{n}$ $n = \frac{360^{\circ}}{40^{\circ}}$ $n = 9$ We can find the interior angle of this polygon: $\frac{(n-2)(180^{\circ})}{n} = \frac{(9-2)(180^{\circ})}{9} = 140^{\circ}$ We can find the exterior angle of this polygon: $360^{\circ} - 140^{\circ} = 220^{\circ}$

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