As per the diagram there are two pairs of vertically opposite angles.
and we know that vertically opposite angles are equal.
$$y = 25^o$$
$$x^o = z^o$$
and we know that. sum of all the angles around a point is $$360^o$$.
$$y^o+x^o+25^o+z^o=360^o $$
$$25^o+x^o+25^o+x^o=360^o $$
$$25^o+x^o=180^o $$
$$ \therefore $$ $$x=155^o $$, $$y=25^o $$ and $$z=155^o $$,