
Grandpa Pencil learns the secret of Drawing Polygons 
Regular polygons consist of a range of figures whose sides are equal and fit exactly into a circle. Equilateral triangles and squares are regular polygons as are pentagons, hexagons and nonagons, among others and are extremely difficult to draw unless you know the secret code. If you draw radii, from the centre of a circle, to adjacent corners of your polygon, at the outer edges of the circle, they will form angles, at the centre, of 360 degrees divided by the number of sides. If you draw a square, therefore, the four angles at the centre of the circle will each be 90 degrees (360 divided by 4 equals 90). 
Obviously you will need some method of drawing a perfect circle. Scribe a circle ensuring that you have its centre marked then draw a line from the centre to the outer edge of the circle. Having decided which polygon you need to draw, find the angle that your next radius must be against your first from the table below and, with a protractor and straight edge, draw that radius to the edge of the circle. Continue until all of the radii are drawn then simply join up those lines where they meet the edge of the circle. Now that's difficult isn't it. 
The table, below, gives the angles for some of the polygons.
the Polygon 
of Sides 
(degrees) 
Equilateral Triangle 

Square 

Pentagon 

Hexagon 

Heptagon 

Octagon 

Nonagon 

Decagon 
* fiftyone and three sevenths degrees
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