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

Summary Submit Skip Question

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,

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