year 8 maths

378 Chapter 6 Angle relationships and properties of geometrical figures 1
Key ideas
■ Polygons are shapes with straight sides. They can be convex or non-convex.
• Convex polygons have all vertices pointing outwards.
• Non-convex (or concave) polygons have at least one vertex pointing inwards and at least
one reflex interior angle.
Convex
Non-convex
This means all interior
angles are less than 180°
This means there is at least
one reflex interior angle
■ Polygons are named according to their number of sides.
Number of sides
Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
11 Undecagon
12 Dodecagon
■ The angle sum S of a polygon with n sides is given by the
rule: S = (n − 2) × 180°
■ A regular polygon has sides of equal length and equal
interior angles.
A regular
octagon
Example 6
Finding the angle sum
Find the angle sum of a heptagon.
SOLUTION
S = (n − 2) × 180°
= (7 − 2) × 180°
= 5 × 180°
= 900°
EXPLANATION
A heptagon has 7 sides so n = 7 .
Simplify (7 − 2) before multiplying by 180° .
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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