25. The four straight lines in the diagram are such that $V U=V W$. The sizes of $\angle U X Z$, $\angle V Y Z$ and $\angle V Z X$ are $x^{\circ}, y^{\circ}$ and $z^{\circ}$.
Which of the following equations gives $x$ in terms of $y$ and $z$ ?

A $x=y-z$
B $x=180-y-z$
C $x=y-\frac{z}{2}$
D $x=y+z-90$
$\mathrm{E} \quad x=\frac{y-z}{2}$
25. E The exterior angle of a triangle is equal to the sum of its two interior and opposite angles.
Applying this theorem to triangle $U Z X$ :
$\angle V U W=z^{\circ}+x^{\circ}$.
Similarly, in triangle $W Y X: y^{\circ}=\angle X W Y+x^{\circ}$,
$$
\text { so } \angle X W Y=y^{\circ}-x^{\circ} \text {. }
$$

As $V U=V W, \angle V U W=\angle V W U$ and also $\angle V W U=\angle X W Y$ because they are vertically opposite angles. Therefore $\angle V U W=\angle X W Y$. So $z^{\circ}+x^{\circ}=y^{\circ}-x^{\circ}$ and hence $x=\frac{1}{2}(y-z)$.