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

(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.