1. In the diagram, $\triangle A B C$ has angles that measure $60^{\circ}$, $(5 x)^{\circ}$ and $(3 x)^{\circ}$. What is the value of $x$ ?
1. Since the angles in any triangle add to $180^{\circ}$, then
$$
\begin{aligned}
60^{\circ}+(5 x)^{\circ}+(3 x)^{\circ} & =180^{\circ} \\
60+5 x+3 x & =180 \\
8 x & =120
\end{aligned}
$$
and so $x=15$.
ANSWER: $x=15$