Can someone explain how to do this? my books and don't didn't tell me what i'm supposed to do to solve this.

 x = 50



Explanation:

Let y be the missing interior angle of the quadrilateral.
So angle y is adjacent to angle x. 

Recall that the sum of all four angles of any quadrilateral is 360, so,
40+80+110+y = 360
230+y = 360
230+y-230 = 360-230 ... subtract 230 from both sides
y = 130



Angle y and angle x form a straight angle.
The two angles add to 180 degrees
x+y = 180
x+130 = 180
x+130-130 = 180-130 ... subtract 130 from both sides
x = 50

Perimeter = 2πr/2 + 2r

= πr + 2r

= r(π+2)

= 5.5(3.14 + 2)

= 5.5 x 5.14

= 28.27 cm

Area = πr^2/2

= 3.14 x 5.5 x 5.5/2

= 47.4925 cm^2

Hope this helps!