To find the value of \( x \), we need to consider the relationship between the angles at points B and D. If we assume that points B and D are part of a polygon (for example, a triangle, where the interior angles sum up to 180 degrees), we can set up an equation based on their angle measures.
However, without additional information about the geometric configuration of points B and D, let's assume that the two angles are related in such a way that they could be supplementary (i.e., their sum is 180 degrees).
Set up the equation:
\[ (3x - 7) + (x + 15) = 180 \]
Now, simplify the equation:
\[ 3x - 7 + x + 15 = 180 \]
Combine like terms:
\[ 4x + 8 = 180 \]
Next, subtract 8 from both sides:
\[ 4x = 180 - 8 \] \[ 4x = 172 \]
Now, divide by 4:
\[ x = \frac{172}{4} = 43 \]
So, the value of \( x \) is \( \boxed{43} \).