If you drop a vertical line thru the 38-degree angle, you subdivide that angle into two equal angles of 19 degrees each. You have a 90-degree angle where this vertical line intersects the base.
Recall that the sum of all the interior angles of a triangle is 180 degrees. If you subtract the sum of 19 degrees and 90 degrees from 180 degrees, you'll have a value for x:
180 deg - (109 deg) = 71 deg.
x = 71 degrees.
Another way in which you could find x would be to write the equation
x + x + 38 = 180, or 2x = 142, or x = 71. Again, x = 71 degrees.