Answer
The value of $x$ is $120^{\circ}$.
Work Step by Step
Tangent line is perpendicular to the radius at the point of tangency.
In the quadrilateral, sum of the angle measures is $360^{\circ}$.
$\Rightarrow x^{\circ}+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}$
Add like terms.
$\Rightarrow x^{\circ}+240^{\circ}=360^{\circ}$
Subtract $240^{\circ}$ from both sides.
$\Rightarrow x^{\circ}+240^{\circ}-240^{\circ}=360^{\circ}-240^{\circ}$
Simplify.
$\Rightarrow x^{\circ}=120^{\circ}$.
