Explanation:

∠, the angle symbol

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other.

http://en.wikipedia.org/wiki/Angle

An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle.

The interior bisector of an angle is the half-line or line segment that divides an angle of less than 180° into two equal angles. The exterior bisector is the half-line that divides the opposite angle (of greater than 180°) into two equal angles.

To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of the same size. The intersection of the circles (two points) determines a line that is the angle bisector. (Our solved example in mathguru.com uses this concept)

http://en.wikipedia.org/wiki/Bisection#Angle_bisector

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.