Interior and Exterior Angles

The sum of the interior angles of a polygon is $180(n-2)$ , where $n$ represents the number of sides. The sum of the interior angles of a pentagon (five sides) is equal to $180(5-2)=540^\circ$ . The pentagon is missing one interior angle, which you can call $y$ :

$100^\circ + 120^\circ + 90^\circ + 109^\circ + y= 540^\circ$

$419^\circ + y= 540^\circ$

$y=121^\circ$

The interior and exterior angles of a polygon are supplementary. Therefore,

$121^\circ + x = 180^\circ$

$\boxed{x=59^\circ}$