01 Key Concepts
Polygon
A closed, two-dimensional shape made up of straight sides, with no curves and no gaps.
Naming Polygons by Sides
Triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), and so on.
Regular Polygons
A polygon where all sides are equal length and all interior angles are equal.
Sum of Interior Angles
For any polygon with n sides, the interior angles sum to (n-2)*180°.
Sum of Exterior Angles
The exterior angles of any convex polygon always sum to exactly 360°, regardless of how many sides it has.
02 Key Formulas
- Sum of interior angles = (n-2)*180°
- Each interior angle of a regular polygon = [(n-2)*180°] / n
03 Solved Examples
Example 1 Find the sum of interior angles of a hexagon (6 sides).
- Apply the formula: (n-2)*180 = (6-2)*180 = 4*180.
Answer: 720°
Example 2 Find each interior angle of a regular pentagon (5 sides).
- Sum of interior angles = (5-2)*180 = 3*180 = 540°.
- Divide by 5 sides (since it's regular): 540/5.
Answer: 108° per angle
Example 3 A polygon has interior angles summing to 1080°. How many sides does it have?
- Set up the equation: (n-2)*180 = 1080.
- Divide both sides by 180: n-2 = 6.
- Add 2: n = 8.
Answer: 8 sides (an octagon)
04 Practice Questions
1Find the sum of interior angles of a quadrilateral (4 sides).
360°
2Find the sum of interior angles of an octagon (8 sides).
1080°
3Find each interior angle of a regular hexagon.
120°
4What do the exterior angles of any convex polygon always sum to?
360°
5What is a 'regular' polygon?
One with all equal sides and all equal angles
📄 Polygons — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.