Answer: The correct option is (C) 130°.
Step-by-step explanation: We are given to find the measure of ∠D from the figure, where
[tex]m\angle A=2x+18,~~~\textup{and}~~~m\angle B=9x-14.[/tex]
From the figure, we note that ABCD is a parallelogram.
So, AD is parallel to BC and AB acts as a transversal.
Then, the sum of the measures of angles A and B is equal to 180°, since they are interior angles on the same side of the transversal.
That is,
[tex]m\angle A+m\angle B=180\\\\\Rightarrow 2x+18+9x-14=180\\\\\Rightarrow 11x+4=180\\\\\Rightarrow 11x=180-4\\\\\Rightarrow 11x=176\\\\\Rightarrow x=\dfrac{176}{11}\\\\\Rightarrow x=16.[/tex]
So, the measure of angle B is
[tex]m\angle B=9x-14=9\times 16-14=144-14=130^\circ.[/tex]
We know that the measures of the opposite angles of a parallelogram is 130°, so
the measure of angle D is 130°.
Thus, m∠D = 130°.
Option (C) is CORRECT.
