GHLJ and GSTU are both parallelograms. Why is ∠L ≅ ∠T?

Answer:

By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Since GHLJ is a parallelogram, angle G is congruent to angle L. Since GSTU is a parallelogram, angle G is congruent to angle T. By the transitive property of congruence, angle L must be congruent to angle T.