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.