1. **State the problem:** We are given the measure of an exterior angle of a regular polygon as 18 degrees. We need to find the measure of an interior angle and the number of sides of the polygon. 2. **Recall the relationship between interior and exterior angles:** For any polygon, the interior angle and its adjacent exterior angle are supplementary, meaning they add up to 180 degrees. 3. **Calculate the interior angle:** $$\text{Interior angle} = 180^\circ - \text{Exterior angle}$$ $$= 180^\circ - 18^\circ = 162^\circ$$ 4. **Find the number of sides:** The sum of all exterior angles of any polygon is always 360 degrees. Since the polygon is regular, all exterior angles are equal. $$\text{Number of sides} = \frac{360^\circ}{\text{Exterior angle}} = \frac{360^\circ}{18^\circ} = 20$$ **Final answers:** - Interior angle = $162^\circ$ - Number of sides = 20