Answer
No, they are not similar.
Work Step by Step
The angles of triangle XYZ are equal to half of the arcs XY, YZ, and XZ. Therefore they measure 60$^{\circ}$, 65$^{\circ}$, and 55$^{\circ}$.
m$\angle$C=.5(ZX+XY-YZ)
m$\angle$C=.5(230-130)
m$\angle$C=50$^{\circ}$
Similar triangles have congruent angles. Since m$\angle$C is not equal to the measures of any of the angles in triangle XYZ, the two triangles cannot be similar.
