1. **Problem:** In a pentagonal garden, the exterior angle at one corner measures 50°. Find the interior angle at that corner. 2. **Problem:** In a decagonal plaza, the exterior angle at a corner is 36°. Find the interior angle at that corner. 3. **Problem:** In a hexagonal courtyard, the exterior angle at a corner is 80°. Find the interior angle at that corner. --- **Step 1: Understand the relationship between interior and exterior angles of polygons.** The interior angle and exterior angle at any vertex of a polygon are supplementary, meaning they add up to 180°. Formula: $$\text{Interior angle} + \text{Exterior angle} = 180^\circ$$ This is because the exterior angle is formed by extending one side of the polygon, creating a linear pair with the interior angle. --- **Step 2: Calculate the interior angles for each polygon using the formula.** **For the pentagonal garden:** $$\text{Interior angle} = 180^\circ - 50^\circ = 130^\circ$$ **For the decagonal plaza:** $$\text{Interior angle} = 180^\circ - 36^\circ = 144^\circ$$ **For the hexagonal courtyard:** $$\text{Interior angle} = 180^\circ - 80^\circ = 100^\circ$$ --- **Final answers:** 1. The interior angle at the pentagonal garden corner is $130^\circ$. 2. The interior angle at the decagonal plaza corner is $144^\circ$. 3. The interior angle at the hexagonal courtyard corner is $100^\circ$.