Edexcel IGCSE Maths 复习笔记 4.2.1 Angles in Polygons
What is a polygon?
- A polygon is a flat (plane) shape with n straight sidesFor example:
A triangle is a polygon with 3 sidesA quadrilateral polygon with 4 sides
A pentagon is a polygon with 5 sides
- In a regular polygon all the sides are the same length and all the angles are the same:
A regular polygon with 3 sides is an equilateral triangleA regular polygon with 4 sides is a square
Working with angles in polygons
1. TOTAL OF INTERIOR ANGLES = 180° × (n – 2)
(because the polygon can be split into n -2 triangles)2. TOTAL OF EXTERIOR ANGLES = 360°
(this exterior angles rule is the same for ANY number of sides!)eg For a hexagon (n=6):
a + b + c + d + e + f = 180° × (6 – 2) = 720°
p + q + r + s + t + u = 360°
For REGULAR Polygons:3. EXTERIOR ANGLE = 360 ÷ n4. INTERIOR ANGLE = 180 – Exterior Angle
Make sure you know whether you are dealing with a regular or irregular polygon before you start a question.