1. Angles in regular polygons Be able to find the interior and exterior angles of any regular polygon Be able to calculate the number of sides from the interior angles

2. 3 sides 4 sides 5 sides 7 sides8 sides 6 sides 180° 2 x 180°=360° 3 x 180°=540° 4 x 180°=720° 5 x 180°=900° 6 x 180°=1080° Can you see a link between number of sides and number of triangles made in the shape?

3. Finding Angles in Polygons The angles in a ____ sided shape will equal ____ x 180 (n-2) n To find the sum of the angles in a polygon, take 2 away from the number of sides and multiply by 180

4. Interior and exterior angles The angles INside are INterior angles The angles outside are exterior angles x x x x xx

5. INERIOR ANGLES- Divide the total of the angles by the number of sides EXTERIOR ANGLES= 180 – interior angle

6. Example 1 What is the size of the interior and exterior angles of a 12 sided shape? 12-2=10 10 x 180=1800° (Sum of angles in the shape) 1800 ÷ 12= 150° (size of each interior angle) Exterior angle= 180-150 ° = 30 °

7. Example 2 What is the size of the interior and exterior angles of a 16 sided shape? 16-2=14 14 x 180=2520° (Sum of angles in the shape) 2520 ÷ 16= 157.5° (size of each interior angle) Exterior angle= 180-157.5 ° = 22.5 °

8. Example 3 What is the size of the interior and exterior angles of a 22sided shape? 22-2=20 20 x 180=3600° (Sum of angles in the shape) 3600÷ 22= 163.6° (size of each interior angle) Exterior angle= 180-163.6 ° = 16.4 °

9. Find the exterior and interior angles of a regular shape which has: a)9 sides b)10 sides c)12 sides d)15 sides e)25 sides ANSWERS 1. a)I=140, E=40 b)I=144, E=36 c)I=150, E=30 d)I=156,E=24 e)I=165.6, E=14.4 Questions

10. Finding the number of sides The exterior angles of a regular polygon will always add up to 360°, so 360°÷ (exterior angle)= number of angles / number of sides

11. Example 1 A regular polygon has exterior angles which are all 36 °, how many sides does it have 360÷ 36= 10 sides A regular polygon has interior angles which are all 108°, how many sides does it have 180 – 108= 72 (size of exterior angle) 360÷ 72= 5 sides Example 2

12. 1. How many sides does a regular polygon have if it’s exterior angles are: a)45 b)40 c)30 d)22.5 e)20 f)3 ANSWERS 1. a)8 b)9 c)12 d)16 e)18 f)120 Questions 2. How many sides does a regular polygon have if it’s interior angles are: a)150 b)156 c)157.5 d)162 e)165 f)168.75 ANSWERS 2. a)12 b)15 c)16 d)20 e)24 f)32