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An angle bisector is a line or ray that divides an angle into two congruent angles .
In the figure, the ray bisects the angle .
The angles and are congruent.
So, .
Note that any point on the angle bisector is equidistant from the two sides of the angle. Some textbooks call this Angle Bisector Theorem , but this name is usually used for another theorem about angle bisectors in a triangle.
Example :
In the figure, is an angle bisector. Find the measure of .
Since is an angle bisector,
Therefore,
By the Angle Addition Postulate,
.
Substitute.