$\underline{\mathbf{Answer: D}}$
$\underline{\mathbf{Explanation:}}$
This is a very easy example of $\mathbf {SOT}$.
$\mathrm{(a+b+c) (a+b-c) = ab\;\;\;[Given]\\(a+b)^2 -c^2 = ab\;\;\;[Using\; Identity \;a^2-b^2 = (a+b) (a-b)] \\ a^2 + b^2 +2ab -c^2 = ab \\ \because a^2 + 2ab + b^2 = (a+b)^2 \\ \therefore a^2 + b^2 -c^2 = ab – 2ab \\ \Rightarrow a^2 + b^2 -c^2 = -ab \\ \Rightarrow \frac{a^2+b^2 -c^2}{ab} = -1}$
Dividing both sides by $2$, we get:
$\mathrm{\frac{a^2+b^2 -c^2}{2ab} = \frac{-1}{2}}$
$\mathrm{\Rightarrow \cos C = \frac{-1}{2} \\ \Rightarrow \cos C = \cos120^0 = \cos\frac{2\pi}{3} \\ \Rightarrow C = \frac{2\pi}{3}}$
$\therefore \mathbf D$ is the correct answer.