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?

Step 1: Identify the type of quadrilateral. 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.

Step 2: Find the value of angle $R$. In a square, the diagonals intersect at right angles. Angle $R$ is formed by the intersection of the diagonals. Therefore, $R = 90^\circ$.

Step 3: Find the value of angle $x$. 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. $x = \frac{90^\circ}{2}$ $x = 45^\circ$

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