Question

Find the angle whose complement is itself.

Answer 1

Let the measure of an angle be $x^{\circ }$, then the measure of its complement is also $x^{\circ }$

We know that the sum of the measures of an angle and it's complementary is ${90}^{\circ }$

$\therefore x^{\circ }+x^{\circ }={90}^{\circ }$

$\Rightarrow 2x^{\circ }={90}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{90}^{\circ }}{2}={45}^{\circ }$