Triangle A B C is shown with centroid G. Lines are drawn from each point of the triangle through the centroid and to the midpoint of the opposite side to form line segment A D, line segment B E, and line segment C F. The length of line segment D G is x minus 15 and the length of line segment G A is x + 7.
G is the centroid of triangle ABC.

What is the value of x?

What is the length of segment DG?
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What is the length of segment AG?
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What is the length of segment AD?
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