Question
Two supplementary angles are in the ratio $3: 7$, find the angles.
✓
Answer
Let the two supplementary angles be $3 x$ and $7 x$.
$
\therefore 3 x+7 x=180^{\circ}
$
$\left[\because\right.$ the sum of two supplementary angles $=180^{\circ}$ ]
$
\begin{array}{l}
\Rightarrow 10 x=180^{\circ} \\
\Rightarrow x=\frac{180^{\circ}}{10} \Rightarrow x=18^{\circ}
\end{array}
$
So, the angles are $3 \times 18=54^{\circ}$ and $7 \times 18=126^{\circ}$
$
\therefore 3 x+7 x=180^{\circ}
$
$\left[\because\right.$ the sum of two supplementary angles $=180^{\circ}$ ]
$
\begin{array}{l}
\Rightarrow 10 x=180^{\circ} \\
\Rightarrow x=\frac{180^{\circ}}{10} \Rightarrow x=18^{\circ}
\end{array}
$
So, the angles are $3 \times 18=54^{\circ}$ and $7 \times 18=126^{\circ}$
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