Final answer:
The Angle Bisector Theorem states that an angle bisector divides the opposite side of a triangle into two segments proportional to the other two sides. However, without more details, we can't solve for the requested missing length in this triangle.
Step-by-step explanation:
The Angle Bisector Theorem states that if a ray or segment bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. If we represent each side of the triangle as a, b, c and the bisected segments as x and y (x being the segment closer to angle 'a'), the theorem is mathematically represented as a/x = b/y.
Given the problem, we assume that the angle bisecting line divides the base of the triangle into two segments of lengths 16 and x, where x is the missing length. Without additional information such as the lengths of the other sides or the proportionality constant, we unfortunately can't provide a numeric solution to this problem. The problem typically provide more details for us to be able to solve for x.
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