Angle subtended by the outside arc is 38 degrees. Inscribed angle x is half of this, or 19 degrees. Angle x also subtends an inside arc of 218 degrees, so x is 360-218 = 142 degrees.
Since O is the center of the circle, the angle formed by the two radii that intersect at O is 180 degrees. Therefore, the angle subtended by the arc on the outside of the circle is 180 - 142 = 38 degrees.
An angle inscribed in a circle subtends half the measure of the central angle that subtends the same arc. Therefore, the inscribed angle x is half the measure of the central angle that subtends the 38-degree arc, which is 38 / 2 = 19 degrees.
However, the inscribed angle x also subtends an arc on the inside of the circle. Since the sum of the measures of the angles inscribed in a circle is 360 degrees, we have the following equation:
19 + 19 + x = 360
Solving for x, we get:
x = 360 - 19 - 19 = 322 degrees
However, since the inscribed angle x subtends an arc on the inside of the circle, we must subtract the measure of that arc from 360 degrees to get the actual measure of angle x. The measure of the arc on the inside of the circle is 360 - 142 = 218 degrees. Therefore, the actual measure of angle x is 360 - 218 = 142 degrees.