Question

An angle is $45°$. Its complementary angle will be _______ .

Answer 1

Complementary Angles.

When the sum of the measures of two angles is $90°$, then the angles are called complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.

Thus, two angles $\alpha$ and $\beta$ are said to be complementary angles if $\alpha +\beta =90°$.

Given, an angle is $45°$. Therefore, let $\alpha =45°$.

Let $\beta$ be the complementary angle of $\alpha$, then

$\begin{array}{rcl}\alpha +\beta & =& 90°\\ & \Rightarrow & 45°+\beta =90°\\ & \Rightarrow & \beta =90°-45°\\ & \Rightarrow & \beta =45°\end{array}$

Hence, the complementary angle of the angle $45°$ will be $45°$.