To determine the value of \( x \), we can start by using the information that angles \( \angle AOC \) and \( \angle COD \) are complementary. This means that the sum of these two angles equals \( 90^\circ \).
Given:
- \( m\angle AOC = 67^\circ \)
- \( m\angle COD = (2x + 3)^\circ \)
Since these angles are complementary, we can set up the equation:
\[ m\angle AOC + m\angle COD = 90^\circ \]
Substituting the given angle values, we have:
\[ 67^\circ + (2x + 3)^\circ = 90^\circ \]
Now, simplify:
\[ 67 + 2x + 3 = 90 \]
Combining constants:
\[ 70 + 2x = 90 \]
Next, subtract 70 from both sides:
\[ 2x = 90 - 70 \]
\[ 2x = 20 \]
Now, divide both sides by 2:
\[ x = 10 \]
Thus, the value of \( x \) is \( 10 \). The correct answer is:
A. 10