To find the measure of ∠D, we start by using the properties of intersecting lines. Angles A and D are vertical angles, meaning they are equal in measure. Therefore, we can set up the equation:
\[ m∠A = m∠D \]
Given that:
\[ m∠A = (4x - 10)° \] \[ m∠D = (2x + 22)° \]
We set the two expressions equal to each other:
\[ 4x - 10 = 2x + 22 \]
Now, we can solve for \( x \):
- Subtract \( 2x \) from both sides:
\[ 4x - 2x - 10 = 22 \] \[ 2x - 10 = 22 \]
- Add 10 to both sides:
\[ 2x = 32 \]
- Divide by 2:
\[ x = 16 \]
Now that we have the value of \( x \), we can substitute it back into the expression for \( m∠D \):
\[ m∠D = 2x + 22 \] \[ m∠D = 2(16) + 22 \] \[ m∠D = 32 + 22 \] \[ m∠D = 54° \]
Thus, the measure of ∠D is \( \boxed{54}° \).