We can construct an angle of 30° by first constructing an angle of 60° then bisecting it. To construct an angle of 60° start by drawing a line AB.

Open the compass to the same length as AB and put the compass needle at B. Draw an arc as shown.

Now put the compass needle at A and draw another arc that crosses the first arc as shown.

The point where the arcs cross is the third vertex of an equilateral triangle, after A and B. Join up the vertices.

Each angle in the triangle is 60 Degrees.

Label the top vertex C. Now bisect the angle BAC.

With the compass at B and C respectively, draw two arcs.

The straight line from A to the point where the lines intersect will form two angles of 30° each at A.