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Geometry, NAP-G3-CA29 SA

All lines of symmetry are drawn on a regular hexagon, pictured below.

What is the size of the angle between each line of symmetry at the centre of the hexagon?
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`30°`

Show Worked Solution

`text(There are 12 equal angles at the centre of the hexagon.)`

`:.\ text(Size of the angle)` `= 360 ÷ 12`
  `= 30°`

Geometry, NAP-B3-CA32

John draws a polygon.

It has a certain number of 110° angles and the same number of 130° angles.

It has no other angles.

The polygon is

`text(a hexagon)` `text(a heptagon)` `text(an octagon)` `text(a decagon)`
 
 
 
 
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`text(a hexagon)`

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`text(The angle sum of the polygon must be a)`

`text(multiple of 240°.)`

`text(Also, the angle sum of any polygon with)\ \ n`

`text(sides)\ = (n-2) xx 180°`

`=>\ text(240° is not possible.)`

`=>\ text(480° is not possible.)`

`=>\ text(720° is possible,)`

`(n-2) xx 180` `=720`
`n-2` `=720/180`
  `=4`
`:. n` `=6`

 

`:.\ text{The polygon is a hexagon (6 sides).}`