Find the angle marked x in this polygon.

To find how many degrees are in a polygon subtract 2 from the number of sides and multiply be 180.
(8 - 2) 180 = 1080.
There are 1080 degrees in the polygon. There are two angle measues missing. The one marked "x" and the one adjacent to the 33-degree angle. Since the angle adjacent to the 33 degree angle forms a line, you can find it by subtracting 33 from 180. The missing angle is 147 degrees. Do the same for the angle adjacent to the 40 degree angle. 
180 - 40 = 140
The other missing angle is 140 degrees.
The last angle we need to know is adjacent to the 144 degree angle. Subtract 144 from 360 to get that angle. 360 - 144 = 216
We now have all of the information we need to solve the problem. The sum of the angle measures of this polygon add up to 1,080 degrees. So, set up the equation. 
x + 74 + 216 + 130 + 147 + 144 + 107 + 140 = 1,080
x = 122

Hope this helps =)