Question
Find an angle which is $2 / 3$ of its complement.
✓
Answer
Let $x$ be the complement of an angle, then the angle will be $\frac{2}{3} x$.
We know that sum of complementary angles is $90^{\circ}$.
$
\begin{array}{lc}
\text { So, } x+\frac{2}{3} x=90^{\circ} \Rightarrow \frac{3 x+2 x}{3}=90^{\circ} \\
\Rightarrow 5 x=270^{\circ} \\
\Rightarrow x=\frac{270^{\circ}}{5}=54^{\circ} \\
\Rightarrow x=54^{\circ} \\
\therefore \frac{2}{3} \times 54^{\circ}=2 \times 18^{\circ}=36^{\circ}
\end{array}
$
Hence, complement angle of $54^{\circ}$ is $36^{\circ}$.
We know that sum of complementary angles is $90^{\circ}$.
$
\begin{array}{lc}
\text { So, } x+\frac{2}{3} x=90^{\circ} \Rightarrow \frac{3 x+2 x}{3}=90^{\circ} \\
\Rightarrow 5 x=270^{\circ} \\
\Rightarrow x=\frac{270^{\circ}}{5}=54^{\circ} \\
\Rightarrow x=54^{\circ} \\
\therefore \frac{2}{3} \times 54^{\circ}=2 \times 18^{\circ}=36^{\circ}
\end{array}
$
Hence, complement angle of $54^{\circ}$ is $36^{\circ}$.
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