To measure an angle, take any convenient radius and describe an arc with the center at the vertex of the angle. The portion of the arc included between the sides of the angle is the measure of the angle. If the are has a constant radius, the greater the divergence of the sides, the longer will be the arc. If there are several arcs drawn with the same center, the intercepted arcs will have different lengths but they will all be the same fraction of the entire circumference.
In order that the size of an angle or arc may be stated without saying that it is a certain fraction of a circumference, the circumference is divided into 360 equal parts called degrees. Fig. 67. Thus, it may be said that a certain angle contains 45 degrees, i.e., it is 45/360 = 1/8 of a circumference. In order to obtain accurate measurements each degree is divided into 60 equal parts called minutes and each minute into 60 equal parts called seconds.
Fig. 67. Angular Measurement.