Figure X is a trapezium and Figure Y is a parallelogram. Which pair of the following statements is true?

1. Evaluate Option (1)

Option (1) states that Figure X has opposite sides that are parallel. Figure X is a trapezium, which has only one pair of parallel sides (top and bottom), not both pairs. Figure Y is a parallelogram, which does have opposite sides parallel. Since the statement for Figure X is false, Option (1) is false.

2. Evaluate Option (2)

Option (2) states that Figure X has one pair of perpendicular lines. Figure X has a vertical left side and a horizontal bottom side, meeting at $\angle b$, which is marked with a right angle. Thus, it has one pair of perpendicular lines. It also states Figure Y does not have any pair of perpendicular lines. Figure Y is a slanted parallelogram with no right angles. Both statements are true, so Option (2) is true.

3. Evaluate Option (3)

Option (3) states $\angle c + \angle d = 180^\circ$ for Figure X. Since the top and bottom sides are parallel, the interior angles on the same side of the transversal sum to $180^\circ$, so $\angle c + \angle d = 180^\circ$ is true. For Figure Y, it states $\angle f + \angle h = 180^\circ$. $\angle f$ and $\angle h$ are opposite angles in a parallelogram, so they are equal, not supplementary (unless it's a rectangle, which it isn't). Thus, Option (3) is false.

4. Evaluate Option (4)

Option (4) states $\angle a + \angle b = 180^\circ$ for Figure X. This is true as they are interior angles between parallel lines. For Figure Y, it states $\angle e + \angle h = 180^\circ$. $\angle e$ and $\angle h$ are adjacent angles on the bottom side, which do not sum to $180^\circ$ (they are not interior angles between parallel lines; rather, $\angle e + \angle f = 180^\circ$ or $\angle e + \angle g = 180^\circ$ if $g$ is adjacent). Thus, Option (4) is false.