Answer:
CG = 8
Explanation:
Given CG = 4x-16 is congruent to AG = 2x -4, you want the value of CG.
Setup
The congruent segments are equal length:
CG = AG
4x -16 = 2x -4
Solution
2x = 12 . . . . . . . . . . add 16 -2x
Substitute into the expression for AG:
2x -4 = 12 -4 = 8
AG is congruent to CG, so ...
CG = 8
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Additional comment
You know triangles GBC and GBA are congruent by the HA theorem, since GB bisects angle ABG. Corresponding parts of congruent triangles are congruent, so CG ≅ AG.