7.06 Angles of polygons
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
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Angle sum of an n-sided polygon is $\left(n-2\right)\times180$(n−2)×180 degrees The angles inside a quadrilateral will add up to $\left(4-2\right)\times180=360$(4−2)×180=360 degrees The angles inside a hexagon will add up to $\left(6-2\right)\times180=720$(6−2)×180=720 degrees The angles inside an octagon will add up to $\left(8-2\right)\times180=1080$(8−2)×180=1080 degrees |
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Sum of exterior angles of any polygon is $360$360°
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Practice questions
Question 1
Neil claims to have drawn a regular polygon with each exterior angle equal to $45^\circ$45°.
First find $n$n, the number of sides of such a polygon.
Hence what type of shapes is this ?
Octagon
ANonagon
BDecagon
CHexagon
DThis shape cannot exist
EHeptagon
F
Question 2
Consider the adjacent quadrilateral.
Find the value of the angle marked $x$x.
Find the value of the angle marked $a$a.
Find the value of the angle marked $b$b.
Find the value of the angle marked $c$c.
Find the value of the angle marked $d$d.
The sum of exterior angles in a quadrilateral is $\editable{}$°