Question

An angle is equal to 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,

$$\begin{gathered} \mathrm{x}°=90°-\mathrm{x}° \\ \Rightarrow \mathrm{x}°+\mathrm{x}°=90° \\ \Rightarrow 2\mathrm{x}°=90° \\ \Rightarrow \mathrm{x}°=\frac{90°}{2} \\ \Rightarrow \mathrm{x}°=45° \end{gathered}$$

Hence, the required angle is $45°$.