Draw the line 0 C about 2 inches long and the line 0 A of about the same length. The angle formed by these lines may be any convenient size - about 45 degrees is suitable. This angle A O C is the given angle.
Now draw F G, a horizontal line about 2 1/4 inches long, and let F, the left-hand extremity, be the vertex of the angle to be constructed with 0 as a center and any convenient radius - about 1 1/2 inches - describe the arc L M cutting both O A and 0 C. With F as a center and the same radius draw the indefinite arc 0 Q. Now set the compass so that the distance between the pencil and the needle point is equal to the chord L M. With Q as a center and a radius equal to L M draw an arc cutting the arc 0 Q at P. Through F and P draw the straight line F E. The angle E F G is the required angle since it is equal to A 0 C.
Since the chords of the arcs L M and P Q are equal, the arcs are equal. The angles are equal because with equal radii equal arcs are intercepted by equal angles.