What is the value of $x$ in the plane figure shown?

[asy]
pair A;
draw(dir(40)--A); draw(dir(200)--A); draw(dir(300)--A);
label("$160^{\circ}$",A,dir(120)); label("$x^{\circ}$",A,dir(250)); label("$x^{\circ}$",A,dir(350));
[/asy]
The angles around a point sum to $360^\circ$, so $x^\circ + x^\circ + 160^\circ = 360^\circ$.  Simplifying gives $2x^\circ + 160^\circ = 360^\circ$, so $2x^\circ = 200^\circ$ and $x=\boxed{100}$.