To determine the value of \( m \) that proves quadrilateral \( ABCD \) is a parallelogram, we typically look at the properties of the opposite sides of the parallelogram. In a parallelogram, the lengths of opposite sides must be equal.
From the numbers provided, it seems we are comparing two pairs of sides represented by the lengths \( 15 \) and \( 18 \), along with \( 7 + m \) and the other side \( 15 \).
To find \( m \), we can set the equation for the opposite sides equal:
\[ 7 + m = 15 \]
To solve for \( m \):
\[ m = 15 - 7 \] \[ m = 8 \]
However, this does not match any of the options provided. If we check \( 7 + m \) against \( 18 \):
\[ 7 + m = 18 \]
Then we would have:
\[ m = 18 - 7 \] \[ m = 11 \]
Thus, to satisfy the conditions of the parallelogram based on the equation of lengths given in the question, the value of \( m \) must be 11.
So, the correct answer is:
11
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