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Constructing a 60°, 30° or 15° Angle

60 degree angle

60 degree angle

Rule

Instructions for Constructing a 60° Angle

1.
Draw a straight line l.
2.
Mark a point called P on the line l.
3.
Put the point of your draft compass on P and make an arc that intersects l and passes above P. Mark a point A where the arc intersects with l.
4.
Without changing the distance between the legs of your draft compass, put the point on A and make a small arc that intersects with the larger arc you made previously.
5.
Draw a line from the point P through the intersection of the two arcs. Ta-da, you’ve got a 60° angle.

Constructing a 30° Angle

If you need to find an angle that is the half the size of another angle, you use the bisection technique. So, if you want to construct a 30° angle, you just construct a 60° angle, and then bisect it. You just make a cross midway between the two sides of the angle and draw a line from the vertex through this cross.

To do this, set the point of your draft compass at A and draw an arc to the right of your existing 60° arc. Keep the distance of the legs of your draft compass, and set the point of the compass at the intersection of the two crossing arcs and the 60° line. From this point, draw a new arc intersecting the arc you marked when the point was set at A. These intersecting arcs should make a cross. Finally, to bisect the 60° angle, draw a straight line from P until this line intersects the newly created cross.

The two new angles are both 30°, because 30 + 30 = 60.

30 degree angle

30 degree angle

Constructing a 15° Angle

To make a 15° angle, you’ll once again need to construct an angle that is half the angle you have just constructed, so you only need to use the bisection technique again. In other words, all you need to do to construct a 15° angle is bisect a 30° angle.

That means you just make a cross midway between the two sides of the angle using a drafting compass and draw a line from the vertex through this cross, using the same instructions as before. The two new angles are both 15°, because 15 + 15 = 30.

15 degree angle

15 degree angle

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