Label the vertices of the quadrilateral A, B, C, D. Angle C is supplementary to the angle of measure 60 degrees, so its own measure is 120 degrees.
AD and BC are parallel, as are AB and CD, so ABCD is a parallelogram. This means angle A also has measure 120 degrees. The angle adjacent to the one with measure [tex]3x[/tex], part of angle A, then has measure [tex]120^\circ-3x[/tex].
The three angles above the line through vertex A are supplementary, so we have
[tex]2x+90^\circ+(120^\circ-3x)=180^\circ[/tex]
[tex]\implies210^\circ-x=180^\circ[/tex]
[tex]\implies x=30^\circ[/tex]
