## Elementary Geometry for College Students (7th Edition)

Published by Cengage

# Chapter 7 - Section 7.3 - More about Regular Polygons - Exercises - Page 344: 38

#### Answer

$36^{\circ}$

#### Work Step by Step

We can find the number of vertices if a regular polygon has 35 diagonals: $\frac{n(n-3)}{2} = 35$ $n(n-3) = 70$ $n^2-3n- 70 = 0$ $(n-10)(n+7) = 0$ $n = 10~~$ or $~~n=-7$ The polygon has 10 vertices. We can find the central angle of this polygon: $\frac{360^{\circ}}{n} = \frac{360^{\circ}}{10} = 36^{\circ}$

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