To find the measure of \(\angle D\), we need to establish a relationship between \(\angle A\) and \(\angle D\). However, you didn't provide any additional information about their relationship such as whether they are congruent, supplementary, or part of a geometric figure like a triangle or quadrilateral.
Assuming \(\angle A\) and \(\angle D\) are supplementary (which is often the case in many problems), we can set up the equation:
\[ m\angle A + m\angle D = 180° \]
Substituting the expressions for the angles:
\[ (4x - 10) + (2x + 22) = 180 \]
Combine like terms:
\[ 6x + 12 = 180 \]
Now, solve for \(x\):
\[ 6x = 180 - 12 \] \[ 6x = 168 \] \[ x = 28 \]
Now, substitute \(x\) back into the expression for \(\angle D\):
\[ m\angle D = 2x + 22 \] \[ m\angle D = 2(28) + 22 \] \[ m\angle D = 56 + 22 \] \[ m\angle D = 78° \]
So, the measure of \(\angle D\) is \(78°\).