If you draw the figure on coordinate plane, you will see that above will be a right angled triangle with 90 degree at vertex (5,1).
The length of perpendicular sides are (y-1) and (5-x).

So area will be ½ * (y-1) * (5-x). To compute this we need both the values of x and y.

Consider first statement (1) alone.
x=y does not give us their individual values.
So (1) alone is not sufficient.
Next consider (2) alone.
Angle at the vertex (x,1) = angle at the vertex (5,y).
This means it is an isosceles right angled triangle.
Or it means the perpendicular sides are same.
Or (y-1) = (5-x).
But again we are not getting the values of x and y individually.
So (2) alone is not sufficient.

Next consider both (1) and (2) combined.
It means x = y and (y-1) = (5-x).
This means y-1 = 5-y.
Or 2y = 6 or y = 3.
So (y-1) = 2.
Or area is ½ * 2 * 2 = 2.

The correct answer is hence (C).