How to draw a 30 degree angle from a 60 degree angle with a compass and ruler only.

In order to draw a 30⁰ degree angle without a protractor first you will need to construct a 60⁰ angle and then bisect this 60⁰ angle. Bisect means cut into two equal halves.

Drawing a 60⁰ angle is quite easy as all you need to do is construct part of an equilateral triangle as the angles in an equilateral triangle are 60⁰

First draw a line 7cm of long (label the start of the line A and the end of the line B).

Next, open your compass to 7cm and draw two arcs from point A and point B above the line AB. Draw a line from point A to the intersection point of the two arcs above the line. You have now made a 60⁰ angle at point A. There is no need to join point B to the intersection point of the two arcs as you are going to make the 30⁰ angle at point A only.

All you need to do now is carry out the angle bisector at A. Open you compass to about 5 cm and draw an arc from point A so that the arcs go across the two lines of the 60⁰ angle. Next draw two further arcs from these two intersection points that you have just made across the angle. These new arcs should intersect each other. Now use your ruler to join point A to the intersection point of the arcs. You have now made the required 30⁰ angle.

You can check how good your compass work is by measuring your final answer with a protractor. So to draw a 30 degree angle remember to construct a 60⁰ angle and cut this angle in half.