1. **Stating the problem:** We want to understand the relationship between interior and exterior angles of polygons with examples. 2. **Formula and rules:** - The sum of the interior angles of an $n$-sided polygon is given by $$\text{Sum of interior angles} = 180(n-2)$$ degrees. - Each exterior angle of a regular polygon is $$\frac{360}{n}$$ degrees. - Interior and exterior angles at the same vertex are supplementary, meaning $$\text{Interior angle} + \text{Exterior angle} = 180^\circ$$. 3. **Example 1: Triangle (3 sides)** - Sum of interior angles: $$180(3-2) = 180^\circ$$. - Each exterior angle (regular triangle): $$\frac{360}{3} = 120^\circ$$. - Each interior angle: $$180 - 120 = 60^\circ$$. 4. **Example 2: Square (4 sides)** - Sum of interior angles: $$180(4-2) = 360^\circ$$. - Each exterior angle (regular square): $$\frac{360}{4} = 90^\circ$$. - Each interior angle: $$180 - 90 = 90^\circ$$. 5. **Example 3: Regular pentagon (5 sides)** - Sum of interior angles: $$180(5-2) = 540^\circ$$. - Each exterior angle: $$\frac{360}{5} = 72^\circ$$. - Each interior angle: $$180 - 72 = 108^\circ$$. 6. **Summary:** For any polygon, the interior and exterior angles at a vertex add up to 180 degrees. Exterior angles always sum to 360 degrees around the polygon. Final answer: Interior and exterior angles are supplementary at each vertex, and exterior angles sum to 360 degrees for any polygon.