Question

An angle is $\frac{2}{3}$ of its complement, then the angle is _______ and its complement angle is _______

Answer 1

$\begin{array}{c}Let{\theta }_1=x\\ {\theta }_2=\frac{2}{3}x\end{array}$

We know that

Sums of complementary angle= ${90}^0$

$\begin{array}{c}\frac{x}{1}+\frac{2}{3}x={90}^0\\ \frac{3x+2x}{3}={90}^0\\ 5x={90}^0\times 3\\ x=\frac{{90}^0\times 3}{5}\\ x=54\\ {\theta }_1=x={54}^0\\ {\theta }_2=\frac{2}{3}x\\ =\frac{2}{3}\times 54\\ ={36}^0\end{array}$

Hence, this is the answer.