What is a polygon?
A polygon is a closed flat shape made of straight line segments called sides. The corners are called vertices. A polygon is named by its number of sides.
| Sides | Name |
| 3 | triangle |
| 4 | quadrilateral |
| 5 | pentagon |
| 6 | hexagon |
A regular polygon has all sides equal and all angles equal.
Sum of interior angles
Key idea / 要点
For a polygon with n sides, the sum of the interior angles = (n − 2) × 180°.
This works because a polygon can be split into (n − 2) triangles, and each triangle has angles adding to 180°. For a regular polygon, each interior angle = the sum divided by n.
Worked example / 例题
Find the sum of the interior angles of a pentagon (5 sides), then each angle if it is regular.
Sum = (n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = 540°.
Regular pentagon: each interior angle = 540° ÷ 5 = 108°.
Check: 5 × 108° = 540°. Correct.
Remember / 记住
- Sum of interior angles = (n − 2) × 180°.
- Regular polygon: every side and every angle is equal.
- Triangle 180°, quadrilateral 360°, pentagon 540°, hexagon 720°.