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
Hour angle is paired with the declination to fully specify the location of a point on the celestial sphere in the equatorial coordinate system. The local hour angle (LHA) of an object in the observer's sky is where LHA is the local hour angle of the object, LST is the local sidereal time, formula_3 is the object's right ascension, GST is Greenwich sidereal time and formula_4 is the observer's longitude (positive east from the prime meridian). These angles can be measured in time (24 hours to a circle) or in degrees (360 degrees to a circle)— one or the other, not both.