Question

An angle is $\frac{4}{5}$ of its complement. What is its magnitude ?

Answer 1

We know that If the sum of the two angles is $90°$, the angles are said to be complementary angles and each angle said to be the complement of the other.

Let $\mathrm{x}°$ be an angle.

Then, the complement of $\mathrm{x}°$ is $90°-\mathrm{x}°$.

Given,

$$\begin{gathered} \mathrm{x}°=\frac{4}{5}\left(90°-\mathrm{x}°\right) \\ \Rightarrow 5\mathrm{x}°=4\left(90°-\mathrm{x}°\right) \\ \Rightarrow 5\mathrm{x}°=360°-4\mathrm{x}° \\ \Rightarrow 5\mathrm{x}°+4\mathrm{x}°=360° \\ \Rightarrow 9\mathrm{x}°=360° \\ \Rightarrow \mathrm{x}°=\frac{360°}{9} \\ \Rightarrow \mathrm{x}°=40° \end{gathered}$$

Hence, the required angle is $40°$.