The angles of a triangle are in the ratio $2: 3: 4$. The largest angle in the triangle is
(A) $100^{\circ}$
(B) $60^{\circ}$
(C) $80^{\circ}$
(D) $90^{\circ}$
(E) $160^{\circ}$
Since the angles are in the ratio $2: 3: 4$, then we can represent the angles as $2 x, 3 x$, and $4 x$ (in degrees) for some number $x$. Since these three angles are the angles of a triangle then

$$
\begin{aligned}
2 x+3 x+4 x & =180^{\circ} \\
9 x & =180^{\circ} \\
x & =20^{\circ}
\end{aligned}
$$

Thus the largest angle is $4 x$, or $80^{\circ}$.

ANSwer: (C)

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