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iGCSE (2021 Edition)

9.06 Angles of polygons

Lesson

Review of 2D shapes

Regular

A regular polygon has all sides (and angles) equal length and size. 

These are all regular polygons.

 

Irregular

An irregular polygon has some sides (and angles) of different lengths and sizes.

These are all irregular polygons.

The word polygon comes from the Greek poly - meaning many and gonos - meaning angles.  So a polygon is a many angled figure.  

With many angles comes many sides, in fact, every 2D straight-sided shape has the same number of angles as sides.  

 

 

Naming 2D shapes

Different sided figures have names that describe the number of angles and sides.  


          


          

           

          

 

Sum of interior and exterior angles of 2D shapes

Angle sum of an n-sided polygon is $\left(n-2\right)\times180$(n2)×180 degrees

The angles inside a quadrilateral will add up to $\left(4-2\right)\times180=360$(42)×180=360 degrees

The angles inside a hexagon will add up to $\left(6-2\right)\times180=720$(62)×180=720 degrees

The angles inside an octagon will add up to $\left(8-2\right)\times180=1080$(82)×180=1080 degrees

Sum of exterior angles of any polygon is $360$360°

 

 

Practice questions

Question 1

Neil claims to have drawn a regular polygon with each exterior angle equal to $45^\circ$45°.

  1. First find $n$n, the number of sides of such a polygon.

  2. Hence what type of shapes is this ?

    Octagon

    A

    Nonagon

    B

    Decagon

    C

    Hexagon

    D

    This shape cannot exist

    E

    Heptagon

    F

Question 2

Consider the adjacent quadrilateral.

  1. Find the value of the angle marked $x$x.

  2. Find the value of the angle marked $a$a.

  3. Find the value of the angle marked $b$b.

  4. Find the value of the angle marked $c$c.

  5. Find the value of the angle marked $d$d.

  6. The sum of exterior angles in a quadrilateral is $\editable{}$°

 

Outcomes

0580C4.7D

Calculate unknown angles using angle properties of regular polygons.

0580E4.7D

Calculate unknown angles using angle properties of regular polygons.

0580E4.7G

Calculate unknown angles using angle properties of irregular polygons.

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