Find the measure of an angle which is 36° more than its complement.

Let the measure of the required angle be $x^{\circ}$

Then, measure of its complement $=(90-x)^{\circ}$.

Therefore,

$x-\left(90^{\circ}-x\right)=36^{\circ}$

$\Rightarrow 2 x=126^{\circ}$

$\Rightarrow x=63^{\circ}$

Hence, the measure of the required angle is $63^{\circ}$.