To solve for the value of \( x \) in the problem, we first need to recognize that the angles \( \angle XOZ \), \( \angle YOZ \), and \( \angle XOY \) are related.
From the given information:
- \( m\angle XOZ = 71^\circ \)
- \( m\angle YOZ = 43^\circ \)
- \( m\angle XOY = (5x + 16)^\circ \)
The angles around point \( O \) must sum up to \( 360^\circ \), but we are looking at only the angles \( \angle XOZ \), \( \angle YOZ \), and \( \angle XOY \). Notably, these three angles should also sum up to \( 180^\circ \) because they form a linear pair:
\[ m\angle XOZ + m\angle YOZ + m\angle XOY = 180^\circ \]
Substituting the known values into the equation gives:
\[ 71^\circ + 43^\circ + (5x + 16)^\circ = 180^\circ \]
Now, we calculate \( 71 + 43 \):
\[ 71 + 43 = 114 \]
The equation now becomes:
\[ 114 + (5x + 16) = 180 \]
Combine like terms:
\[ 114 + 16 = 130 \]
So, we have:
\[ 130 + 5x = 180 \]
Now, isolate \( 5x \):
\[ 5x = 180 - 130 \] \[ 5x = 50 \]
Now, divide by 5:
\[ x = 10 \]
After reviewing the calculations, it seems there may have been an error in interpreting angles based on the requirements of the question. Since the values provided in the answer choices do not include \( 10 \), let's double-check the setup, simplifying our assumptions or aggregation of angles if needed.
If we missed any critical inclusion of angle configuration (like if angles correspond to a broader contextual connection), we need additional placements to reassess to find fundamental alternative angles. Would you kindly clarify or provide any additional angles or relations that would encompass the expected values present in the alternatives more closely? Would be glad to further reassess!