Inscribed angle its intersection points equals half of the central angle subtended by the chord. See also Tangent lines to circles. The inscribed angle theorem is used in many proofs of elementary Euclidean geometry of the plane. A special case of the theorem is Thales' theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. As a consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in a circle. As another example, the inscribed angle theorem is the basis for several
Degree (angle) With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" called "grad" or "gon", where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = gon). Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades () were used with French artillery sights in World War I. An angular mil, which is most used in military applications, has at least three specific variants, ranging from to