#### Answer

(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.