This chapter describes an approach to teaching angle at the beginning of secondary school. Its implementation and its explanation are enriched by historical enquiry using: an article in the Encyclopédie of Diderot and d’Alembert; an extract from the Elémens de Géométrie by Clairaut; early problems from navigation; the measurement of inaccessible distances taken from early guides. For preparing the teaching material, two older school textbooks were consulted. The historical approach suggested refocusing the teaching of angle on the idea of magnitude, using a functional definition and privileging the measurement of angles. Learning had meaning and sense for the students based on activities which, for the most part, were taken from historical documents, namely: constructing the compass rose, drawing spirals, calculating inaccessible distances and finding navigation routes. Through this the students met the bisection and trisection of an angle. The chapter provides a double interest for the history of mathematics: showing the source of the knowledge taught and for understanding the purpose of what is taught.