1. Shape and Space INTERNAL ANGLES

2. POLYGON (REGULAR). A polygon is a two dimensional shape with straight sides. There are two types of polygon, regular and irregular. In a regular polygon each length and angle are equal. Below is a list of the first six regular polygons Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Heptagon Regular Octagon

3. INTERNAL ANGLES What is the sum of internal angles in a square? We can divide a square into two triangles What is the sum of the internal angles of triangle? 180° Two triangles in a square gives a total of 2 × 180 = 360° Size of one internal angle is 360 ÷ 4 = 90° 90°

4. INTERNAL ANGLES What is the sum of internal angles in a pentagon? We can divide a pentagon into three triangles What is the sum of the internal angles of a triangle? 180° Three triangles in a pentagon gives a total of 3 × 180 = 540° Size of one internal angle is 540 ÷ 5 = 108° 108°

5. INTERNAL ANGLES 540 ÷ 5 = 108° 360 ÷ 4 = 90° 180 ÷ 3 = 60° 180 × 3 = 540° 180 × 2 = 360° 180 × 1 = 180° 5 4 3 3 2 1 N - agon Regular Polygon Number of sides Divide into how many triangles? Sum of internal angles Size of one angle TriangleTriangle SquareSquare PentagonPentagon

6. EXERCISES 1. Calculate the internal angle of a regular nonagon (9 sides). 2. Calculate the internal angle of a regular decagon (10 sides). 3. Calculate the internal angle of a regular hendecagon (11 sides). 4. Calculate the internal angle of a regular dodecagon (12 sides). What does the internal angle tend to when the number of sides increase?