Let [tex]z^\circ[/tex] be the measure of the unlabeled arc. Then
[tex]x^\circ+y^\circ+z^\circ=360^\circ[/tex]
The arc with measure [tex]y^\circ[/tex] is subtended by a central angle of 180 degrees. We know this because the chord in the picture passes through the circle's center, so it must be the circle's diameter.
So we have
[tex]x^\circ+z^\circ=180^\circ[/tex]
By the inscribed angle theorem, the inscribed angle of measure 36 degrees has half the measure of the central angle subtended by the same arc. This means [tex]z^\circ=2\cdot36^\circ=72^\circ[/tex].
So
[tex]x^\circ=108^\circ[/tex]
