To find the measure of ∠D, we need to set up an equation using the given information.
We know that m∠A = (4x - 10)° and m∠D = (2x + 22)°.
Since ∠A and ∠D are vertical angles, they have the same measure.
Therefore, we can set up the equation:
(4x - 10)° = (2x + 22)°
Now, we can solve for x:
4x - 10 = 2x + 22
Subtract 2x from both sides:
2x - 10 = 22
Add 10 to both sides:
2x = 32
Divide both sides by 2:
x = 16
Now, substitute the value of x back into the expression for ∠D:
m∠D = (2x + 22)°
m∠D = (2(16) + 22)°
m∠D = (32 + 22)°
m∠D = 54°
Therefore, the measure of ∠D is 54°.