It is assumed the given figure is a parallelogram.
Use properties of a parallelogram:
- opposite sides are parallel and congruent,
- diagonals bisect each other.
Find the missing values:
- ML = NP = 12 m, opposite sides are congruent,
- LP = MN = 10 m, opposite sides are congruent,
- m∠LPM = m∠NMP = 62°, alternate interior angles are congruent, as LP║MN and MP is transversal,
- LN = LQ*2 = 9*2 = 18 m, as Q is the midpoint of LN,
- m∠MLN = m∠PNL = 32°, alternate interior angles are congruent, as ML║NP and LN is transversal,
- QN = QL = 9 m, as Q is the midpoint of LN.