# Chapter 7 - Test - Page 339: 13

(a) This regular polygon has 10 sides. (b) This regular polygon has 35 diagonals.

#### Work Step by Step

(a) We can find the number of vertices of this polygon: $36^{\circ} = \frac{360^{\circ}}{n}$ $n = \frac{360^{\circ}}{36^{\circ}}$ $n = 10$ Since the number of sides is equal to the number of vertices, this regular polygon has 10 sides. (b) We can find the number of diagonals: $\frac{n(n-3)}{2} = \frac{(10)(10-3)}{2} = 35$ This regular polygon has 35 diagonals.

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