Answer:
- not possible
- the locations of the vertices of the marked angles need to be known relative to the arc subtended by the 34° angle.
Explanation:
Angle X depends on the separation of the parallel lines, and on the relative sizes of the longer arcs.
As is, there is insufficient information to find x.
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Label the points of intersection of the line segments with the circle A-D clockwise from the vertex of the 34° angle. Then, knowing the measures of either of the arcs adjacent to A, and either of the arcs adjacent to C will be sufficient to determine angle X.
If the line at C is extended across the circle to intersect at E, arcs CB and EA are congruent. The measure of angle X is the sum of arc CB and half of arc AB.