Question

Find the measure of an angle which is equal to its complement?

Answer 1

Find the measure of an angle with the given condition

If the sum of two angles is equal to $90°$, then the angles are known as complementary angles.

If the value of one angle is given, let us assume that value is $x°$.

Then, the complementary angle of the given angle can be given by $90°-x°$.

The given condition is the measure of the angle and the complementary angle is equal.

Thus, $x°=\left(90°-x°\right)$

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

Therefore, the measure of the angle which is equal to its complement is $45°$.