The diagram shows a quadrilateral with diagonals intersecting at R. One angle is 45 degrees and some sides are marked as equal. What is the measure of angle X?

The image shows a quadrilateral with four equal sides (indicated by the single tick marks on each side) and one right angle at a vertex (indicated by the square symbol). A quadrilateral with four equal sides and one right angle is a square.

In a square, the diagonals intersect at right angles. Angle $R$ is formed by the intersection of the diagonals.
Therefore, $R = 90^\circ$.

In a square, the diagonals bisect the vertex angles. Each vertex angle of a square is $90^\circ$. Angle $x$ is formed by a diagonal and a side, which is half of a vertex angle.

The unknown angles are:
$R = \boxed{90^\circ}$
$x = \boxed{45^\circ}$