If the exterior angle of a regular polygon is $18^\circ$, then find the number of diagonals in this polygon.

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**Solution:**

1. Given each exterior angle of the polygon is $18^\circ$.

2. The sum of all exterior angles of any polygon is always $360^\circ$.

3. Number of sides $n$ of the polygon is given by:

$$n = \frac{360^\circ}{18^\circ} = 20$$

4. The formula for the number of diagonals in a polygon with $n$ sides is:

$$	ext{Number of diagonals} = \frac{n(n - 3)}{2}$$

5. Substitute $n = 20$:

$$\frac{20 	imes (20 - 3)}{2} = \frac{20 	imes 17}{2} = 10 	imes 17 = 170$$

**Answer:** $170$

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