Drawing things using angles

The building blocks of everything you'll ever draw are composed of simple shapes like squares and triangles, however sometimes you need to use more complex shapes like pentagons or hexagons to make drawing something easier. These more complicated designs are hard to draw perfectly, but there's always a way to make things easier. In cases like these, drawing by measuring the angles is a useful way to create any regular shape with ease. This sort of thing works best in a vector art program where the ends of the lines can be made to 'snap' together, but it works in any media. The instructions are a little more complex for drawing things on paper, so this page separates them out.

On a computer...

First, draw one side of the figure you are going to make. The length of the line depends on what you're drawing; for example an octagon's bottom side is one third of the total width of the octagon.
Now, copy that line. Use your editor's "copy" command so that one copy of the original line remains in the clipboard.
Rotate your copied line by a certain amount (see table below) and place one end of the rotated line on the end of the original line.
Continue to paste and rotate until your design comes all of the way around and meets itself. If the angles were correct, the last line will perfectly fit between the first line and the second to last line with no overlap.

By hand...

Using angles when drawing by hand is a bit tricky, as you need to pay more attention to what you're doing. You'll also need a ruler and protractor (or just a protractor with a ruler on one side). First, draw one side of your shape. As mentioned above, the length of the line depends on what you're drawing.
Measure your line and either mark down how long it is or be prepared to memorize it for a bit.
Using the protractor and ruler, draw another line at the angle specified by the chart below. This new line should be the same length as the first and starts where the first line ended.
Continue measuring the angle and drawing new lines until you wind up at the start of the first line.

Angle Chart

Equilateral triangles 3 60°
Squares or rectangles 4 90°
Pentagons 5 108°
Hexagons 6 120°
Heptagon (aka Septagon) 7 128.6°
Octagon 8 135°
Nonagon 9 140°
Decagon 10 144°
Hendecagon 11 147.27°
Dodecagon 12 150°
Hexadecagon 16 157.5°
Icosagon 20 162°