Chapter 16 · ICSE Class 8 Mathematics

Understanding Shapes (Including Polygons)

Explore polygons in depth — their angle sums, and the special rules for regular polygons.

🔷 Chapter 16

Four polygon types: triangle, quadrilateral, pentagon, and hexagon Four polygons shown side by side with their number of sides: a triangle with 3 sides, a quadrilateral with 4 sides, a pentagon with 5 sides, and a hexagon with 6 sides Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6)
16.1

Angle Sum of a Polygon

The sum of interior angles of a polygon with n sides is (n−2) × 180°. This works for any polygon, no matter how irregular its shape.

1

Find the sum of interior angles of a pentagon (5 sides).

(5−2) × 180° = 3 × 180° = 540°

2

Find the sum of interior angles of a hexagon (6 sides).

(6−2) × 180° = 4 × 180° = 720°

16.2

Regular Polygons

In a regular polygon, all sides and all angles are equal. Each interior angle can be found by dividing the total angle sum by the number of sides: (n−2) × 180° ÷ n.

1

Find each interior angle of a regular hexagon.

(6−2) × 180° ÷ 6 = 720° ÷ 6 = 120°

2

Find each interior angle of a regular octagon.

(8−2) × 180° ÷ 8 = 1080° ÷ 8 = 135°

Practice

Exercises

1. Find the sum of interior angles of a heptagon (7 sides).

2. Find the sum of interior angles of an octagon (8 sides).

3. Find each interior angle of a regular pentagon.

4. Find each interior angle of a regular decagon (10 sides).

5. A polygon has an interior angle sum of 1260°. How many sides does it have?

Next chapter — Chapter 17: Special Types of Quadrilaterals ◆ →