To solve for the value of \( x \) given \( m∠XOZ = 71° \), \( m∠YOZ = 43° \), and \( m∠XOY = (5x + 16)° \), we can use the fact that the angles around point O must add up to 360°.
First, we will find \( m∠XOY \) using the relationship between the angles:
\[ m∠XOZ + m∠YOZ + m∠XOY + m∠YOX = 360° \]
Since we don't have \( m∠YOX \) but we can express it in terms of \( m∠XOY \):
\[ m∠YOX = 360° - (m∠XOZ + m∠YOZ + m∠XOY) \]
To simplify, let's add \( m∠XOZ \) and \( m∠YOZ \):
\[ m∠XOZ + m∠YOZ = 71° + 43° = 114° \]
Now, since \( m∠XOY = (5x + 16)° \), we can set up the equation:
\[ m∠XOY + m∠XOZ + m∠YOZ = 360° \]
Substituting in the known angles:
\[ (5x + 16) + 71 + 43 = 360 \]
Simplifying this gives:
\[ 5x + 130 = 360 \]
Now, subtract 130 from both sides:
\[ 5x = 360 - 130 \]
\[ 5x = 230 \]
Now divide both sides by 5 to solve for \( x \):
\[ x = \frac{230}{5} = 46 \]
It appears there may be an oversight since this does not match the options provided.
We will instead focus on seeing whether \( m∠XOY \) can be related directly from \( m∠XOZ \) and \( m∠YOZ \).
Since these angles fit into the setup of adjacent angles:
We actually need:
\[
m∠XOY = m∠XOZ + m∠YOZ
\]
Therefore:
\[ (5x + 16) = 71 + 43 \]
Thus:
\[ (5x + 16) = 114 \]
\[ 5x = 114 - 16 \]
\[ 5x = 98 \]
Dividing both sides by 5:
\[ x = \frac{98}{5} = 19.6 \]
Thus, the correct answer is \( \boxed{19.6} \) (option B).