Angles in regular polygons

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Presentation transcript:

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

3 sides 4 sides 5 sides 180° 2 x 180°=360° 3 x 180°=540° 7 sides Can you see a link between number of sides and number of triangles made in the shape? 7 sides 8 sides 6 sides 5 x 180°=900° 4 x 180°=720° 6 x 180°=1080°

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

Interior and exterior angles The angles INside are INterior angles The angles outside are exterior angles

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

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 °

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 ÷ 14= 157.5° (size of each interior angle) Exterior angle = 180-157.5 ° = 22.5 °

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 °

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

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

Example 1 A regular polygon has exterior angles which are all 36 °, how many sides does it have 360÷ 36= 10 sides Example 2 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

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