A rectangular piece of paper was folded at two of its corners F and H as shown.

1. Identify the relationship between the angles at corner K before and after folding.

When the corner of the rectangular paper at $K$ is folded, the crease line is $LK$. The original corner angle $\angle DKJ = 90^\circ$ is folded over.
Since the corner is folded along $LK$, the angle $\angle LKH$ is equal to the original unfolded angle $\angle LKD$.
Therefore, $\angle LKD = \angle LKH$.

2. Calculate the angle $\angle HKJ$.

We are given that the angle between the fold line $LK$ and the vertical edge $KJ$ is $\angle LKJ = 67^\circ$.
Since the corner of the rectangle is $90^\circ$, we have:
$\angle LKD = 90^\circ - \angle LKJ = 90^\circ - 67^\circ = 23^\circ$
Since the fold is symmetric, the angle $\angle LKH = \angle LKD = 23^\circ$.
Thus, we can find $\angle HKJ$:
$\angle HKJ = \angle LKJ - \angle LKH = 67^\circ - 23^\circ = 44^\circ$

(Alternative approach):
Let the crease line be $LK$. The total angle at $K$ of the unfolded sheet is $90^\circ$.
When folded, the angle $\angle DKL$ (which is $90^\circ - 67^\circ = 23^\circ$) is folded over to become $\angle HKL = 23^\circ$.
Thus, $\angle HKJ = \angle LKJ - \angle HKL = 67^\circ - 23^\circ = 44^\circ$.

1. Calculate $\angle DLF$ using angles on a straight line

Since D, L, and K lie on the straight top edge of the rectangular paper, DLK is a straight line (partially folded but the edge line remains straight before the crease). The angle given is $\angle FLK = 157^\circ$ (or the angle between the top horizontal edge and the crease/line is $157^\circ$). Thus, the adjacent angle on the straight line $\angle DLF$ is calculated by:
$\angle DLF = 180^\circ - 157^\circ = 23^\circ$

1. Identify the definition of a trapezium and check the parallel conditions of DEFL.

A trapezium is a quadrilateral with at least one pair of parallel sides.

• $DL$ is a segment along the horizontal top edge $DK$.
• $EF$ is a diagonal line segment connecting the left edge to the top edge, so it is not horizontal and thus not parallel to $DL$.
• $DE$ is a segment along the vertical left edge $DG$.
• $FL$ is part of the line $LJ$ which is slanted and not vertical, so it is not parallel to $DE$.

Since no pair of opposite sides in $DEFL$ is parallel, $DEFL$ is not a trapezium because $DL$ is not parallel to $EF$ (and $DE$ is not parallel to $FL$).