AN'GLE (Lat. angulus. a corner, Gk. ard7.oc, ankylos. bent). One of the common geometric concepts. If two lines meet, they are said to form on angle, the lines being called the arms, sides, or legs, and the point of meet ing the vertex of the angle. The size of the angle is determined by the amount of turning necessary to carry a moving radius from one arm to the other, and hence is independent of the length of the arms.
If the arms of an angle are in the same straight line on opposite sides of the vertex, a the other two cells are the sperms. The embryo sac within the ovule, which represents a single unshed spore, produces within itself a group of cells, usually seven in number, which represent a reduced female plant. In the end of the sae toward the mieropyle (the opening left by in tegument) the single egg is situated, and asso straight angle (fig. 1) is formed; half of a straight angle is called a right angle (fig. 2) two straight angles equal a perigon or angle of 360° (fig. 3). Angles are also conceived exceed ing 360'; thus an angle of 720° is described when a screw is turned twice around. An angle between 0° and 90° is said to be acute (fig. 4) ; one between 90° and 180°, obtuse (fig. 5) ;
one between ISO° and 360°. reflex (fig. 6). An gles are considered as positive if generated by a radius moving counter-clockwise, and negative if the radius moves clockwise. ff the arms arc strai.dit, the angle is said to be •r•titincar; if curved. currilinear ; if arc's of great circles on a sphere. spherical. Curvilinear angles have the same measure as the rectilinear angles formed by tangents to the curves at the vertex. if two planes meet, they are said to form a dihedral (Gk. two-seated) angle; this has the same measure as the rectilinear angle formed by two lines in the planes that are per pendieular to the line of intersection of the planes. If three or more planes meet in one point. they are said to form a so/id angle, the measure of which is the ratio of the intercepted surface to the entire surface of any sphere hav ing the vertex of the angle as its centre. A solid angle is t rihed ral, let nahcrlrel, ete., accord ing as it is formed by 3, 4, etc., planes. For the various attempts made to define the simple con cept angle, consult Sehotten, and He Mode des planimet•ischen Unit rrich t s (Leipzig, 1893).