To find the measure of \( \angle D \), you'll need to set up an equation involving both angles \( \angle A \) and \( \angle D \) since they are expressed in terms of \( x \).
If you know that \( \angle A \) and \( \angle D \) are related in a specific way (such as supplementary or equal), you can use that information to solve for \( x \). However, without additional information, let's assume \( \angle A \) and \( \angle D \) are equal:
\[ m\angle A = m\angle D \]
This gives us the equation:
\[ 4x - 10 = 2x + 22 \]
Now, solve for \( x \):
- Subtract \( 2x \) from both sides:
\[ 4x - 2x - 10 = 22 \]
This simplifies to:
\[ 2x - 10 = 22 \]
- Add 10 to both sides:
\[ 2x = 32 \]
- Divide both sides by 2:
\[ x = 16 \]
Now, substitute \( x \) back into the expression for \( m\angle D \):
\[ m\angle D = 2x + 22 = 2(16) + 22 = 32 + 22 = 54^\circ \]
Thus, the measure of \( \angle D \) is \( 54^\circ \).