In triangle $ABC$ above, side $\overline{AC}$ is extended to point $D$. What is the value of $y-x$ ?

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We can first sum up the three angles of the triangles to find $x$.

$$32\degree + 116\degree+ x\degree = 180 \degree$$ $$x = 32 \degree$$

$x$ and $y$ lie on the same line, are are therefore supplementary:

$$x+y=180$$ $$32+y=180$$ $$y=148$$

Finally,

$$y-x$$ $$= 148-32$$ $$=\boxed{116}$$