Find the value of x. The diagram shows a polygon.

$$(2x - 50)^\circ + (x + 40)^\circ + (x + 20)^\circ + 80^\circ + 160^\circ + 90^\circ = 720^\circ$$

Combine $x$ terms: $2x + x + x = 4x$.
Combine constant terms: $-50 + 40 + 20 + 80 + 160 + 90$.

$$-50 + 40 = -10$$ $$-10 + 20 = 10$$ $$10 + 80 = 90$$ $$90 + 160 = 250$$ $$250 + 90 = 340$$

So the equation becomes:

$$4x + 340^\circ = 720^\circ$$

$$4x = 720^\circ - 340^\circ$$ $$4x = 380^\circ$$

$$x = \frac{380^\circ}{4}$$ $$x = 95^\circ$$

The value of $x$ is $\boxed{95^\circ}$.