To find the sum of the interior angles of a quadrilaterals, divide it up into triangles... There are two triangles...  Because the sum of the angles of each triangle is 180 degrees...  We get

So, the sum of the interior angles of a quadrilateral is 360 degrees.

To find the measure of the interior angles, we know that the sum of all the angles is 360 degrees (from above)...  And there are four angles...

So, the measure of the interior angle of a square is 90 degrees.

So, the measure of the central angle of a square is 90 degrees.