A quadrilateral has all its four angles of the same measure.

Let $x$ be the measure of each angle.

Since, the sum of all the angles of a quadrilateral is $360^{\circ}$, we have:

$x^{\circ}+x^{\circ}+x^{\circ}+x^{\circ}=360^{\circ}$

$\Rightarrow 4 x^{\circ}=360^{\circ}$

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

$\therefore$ The measure of each angle is $90^{\circ}$.