To find the value of angle D, we first need to determine the value of \( x \) by using the information about the interior angles at points B and D.
From the problem, we have:
- Angle at point B: \( 3x - 7 \)
- Angle at point D: \( x + 15 \)
Assuming that points B and D are part of a polygon and the sum of the interior angles at these points equals 180 degrees (as a simple case), the equation would be:
\[ (3x - 7) + (x + 15) = 180 \]
Now we simplify and solve for \( x \):
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Combine like terms: \[ 3x - 7 + x + 15 = 180 \] \[ 4x + 8 = 180 \]
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Subtract 8 from both sides: \[ 4x = 172 \]
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Divide by 4: \[ x = 43 \]
Now that we have the value of \( x \), we can find the measure of angle D using the expression for angle D:
\[ D = x + 15 = 43 + 15 = 58 \]
However, since none of the provided options match 58. It's possible that the angles at points B and D should sum to a different value, or another condition needs to be applied.
For just angle D from the provided options and if we assess it using typical angle measures:
Attempting again with refreshing \( x \). If you mean that angles \( 3x - 7 \) and \( x + 15\) are simply equal for contrast or a smaller polygon's angle:
If they need to be equal: \[ 3x - 7 = x + 15 \]
- Rearranging gives: \[ 3x - x = 15 + 7 \] \[ 2x = 22 \] \[ x = 11 \]
Then now substituting for angle D: \[ D = 11 + 15 = 26 \]
Checking the options, angle D is \( 26 \).
Thus, the correct answer is: 26.