Polygons
Closed figures formed by straight line segments — classified by number of sides, regularity, and interior angle sums.
A polygon is a closed, flat shape made entirely of straight line segments. The segments are the sides, and the points where sides meet are vertices.
Polygons are named by their number of sides:
| Sides | Name |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 10 | Decagon |
| 12 | Dodecagon |
A polygon is regular if all its sides are equal and all its angles are equal. A polygon is convex if all interior angles are less than — no vertex "caves in." Otherwise it is concave.
The interior angles of any polygon with sides always add up to:
A triangle: . A quadrilateral: . A pentagon: . Each new side adds another .
A stop sign is a regular octagon ().
Sum of interior angles: .
Each interior angle: .
The interior angles of a hexagon are , , , , , and one unknown. Find the unknown angle.
Solution
Interior angle sum for a hexagon: .
Unknown .