The measure of the angle which is equal to its complementary angle is _____.

The correct option is C

${45}^{\circ }$

Let one of the angle be $x^{\circ }$.

Then, the complementary angle is also $x^{\circ }$ [Given that angles are equal]

$x+x={90}^{\circ }$ [ Sum of two complementary angles is ${90}^{\circ }$]

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

$\Rightarrow x={45}^{\circ }$

So, the angle whose complementary angle is itself is ${45}^{\circ }$.