Marking 60° , 30° , and 15° Angles

The first time I saw a compass, the kid next to me was drawing
pretty designs like this with it. My mother got plenty of
these whimsical paper flowers over the next few days. They
were easy to draw since the compass never had to be reset.
The same compass setting used to draw the circle was also
used to mark the flower out. It was many years later before I
realized that the same design was also the layout for dividing a
circle into six equal parts.

This practice is designed to show how to mark 60° , 30° and 15° angles. You can mark any of these angles from a straight line using a compass and starting with a 60° angle.

First: Draw a straight line of any length and mark
a point on the line close to the center. Set your
compass point on the marked point and draw
a semi-circle or half of a circle.

Second: Leave the setting of the compass the
sameas above and place the compass point where
the semi-circle and the straight line meet. Mark a
small arc across the semi-circle.

Third: Draw a line from the center point
of your straight line to the mark on the semicircle.
The line is 60° from the bottom line.

To mark a 30° angle, divide the sixty degree angle in half ( bisect the angle). Since all points on the semi-circle are equal distance from the center, all you have to do to bisect the angle is:

First: Keep your compass setting the same
and place the compass on the point where
the semi-circle and one of the straight lines
of the 60° angle meet. Mark an arc above,
but within the boundaries of the 60° angle.
Repeat the same action for the other 60° angle line.

Second: Draw a straight line from the center
point of the straight line (vertex of the 60° angle)
to where the arcs cross. This causes the 60° angle
to be bisected and results in two 30° angles.

To mark a 15° angle, keep the compass setting the same and bisect one of the 30° angles.