LO – Understand and apply the formulae used to find Interior and Exterior angles in regular Polygons

Name______

The size of the exterior angle of a hexagon is______and its interior angle is______This tells me that interior and exterior______angles______because______

______

I can apply this knowledge to all regular/irregular polygons. (Deleteincorrect answer)

The formula I can use to find the size of ONE exterior angle of a polygon is ______and if it’s regular I can just______If I know the value of one interior angle I can multiply this by ______to find the sum of interior angles assuming its regular/irregular (delete incorrect answer)

Based on what I have just learnedMy Formulae for Regular polygons are:

One Exterior angles______

One interior angle______

Sum of Interior Angles______

Complete the following table

Shape / Number of sides / Size of each Interior Angle / Size of each Exterior Angle / Sum of interior angles
Hexagon
5
90 / 90
180º
Heptagon
8
Icosagon (Google it)

Show the interior and exterior angles on the following shapes. They are not drawn accurately and you will use you knowledge about angle facts rather than measuring the angles (write answers inside or next to shape)

Extension – Write about the way you would deal with finding interior and exterior angles in irregular polygons (do it on the back of the sheet) and try and articulate your answer to share with the class

ANSWERS

Please note – the language use in this sheet is aimed at KS3/GCSE foundation level

The size of the exterior angle of a hexagon is 60º and its interior angle is 120º .This tells me that interior and exterior angles add to 180º because they are on a straight line (or supplementary)

I can apply this knowledge to all regular polygons.

The formula I can use to find the size of ONE exterior angle of a polygon is 360º/n (where n is the number of sides) and if it’s regular I can just divide this equally.

If I know the value of one interior angle I can multiply this by n (the number of sides) to find the sum of interior angles assuming its regular

Based on what I have just learnedMy Formulae for Regular polygons are:

One Exterior angles 360º/n (360 degrees divided by the number of sides)

One Interior angle 180º - Exterior and angle (think straight line angles = 180 degrees)

Sum of Interior Angles n(value of one interior angle) (number of sides x size of interior angle)

Complete the following table

Shape / Number of sides / Size of each Interior Angle / Size of each Exterior Angle / Sum of interior angles
Hexagon / 6 / 120º / 60º / 720º
Pentagon / 5 / 108º / 72º / 540º
Quadrilateral / 4 / 90 / 90 / 360º
Triangle / 3 / 60º / 60120º / 180º
Heptagon / 7 / 128.57º / 51.43º / 900º
Octagon / 8 / 135º / 45º / 1080º
Icosagon (Google it) / 20 / 162º / 18º / 3240º

Show the interior and exterior angles on the following shapes. They are not drawn accurately and you will use you knowledge about angle facts rather than measuring the angles

Mark extension with ‘professional judgement’(and actively encourage pupils to have a go)