Angles are formed by the convergence of two straight lines, or more precisely by the rotation of a straight line about a fixed point, and the method of bisecting them is shown in 341:1 where an arc is struck from centre A and further equal arcs from B and C. From the point at which these two arcs intersect a line drawn to A will bisect the angle. This method can be used to strike all the commonly used angles, e.g. a right angle of 90° can be bisected to produce a true mitre of 45° and again bisected to produce a half-mitre of 221/2°. Angles of 60° can be struck by describing an arc BC from A (341:2) and a similar arc AC from B. If lines are drawn from C to A and B then the figure thus formed will be an equilateral triangle with all sides and all angles equal. As the sum of the angles contained in a triangle must equal 180°, then each angle will be 60°, and bisecting them further gives angles of 30°.

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