Step-by-step explanation:
(1)
FP = FN
makes the triangle FNP an isoceles triangle (both legs have the same length). and that means both angles of these equal legs with the third side (PN) must be equal.
therefore, the angle N = P2 = 56°.
and we know that the angle P = P1 + P2 = 68 + 56 = 124°.
LE = LM
makes the triangle ELM an isoceles triangle. because of that, both angles of these 2 legs with the third side (ME) are equal.
therefore, M1 = E1 = 62°.
the fact that the sum of all angles in a triangle is always 180° gives us the angle L
180 = 62 + 62 + angle L = 124 + angle L
56° = angle L
because angles L and P are supplementary (that means together they have 180°, which is true as 124 + 56 = 180), it means that LM || PN. as this pair of supplementary angles means that their connecting line LP is intersecting the lines LM and PN at the same angles, which makes LM parallel to PN.
and as angle N = angle L (56°), this also proves that MN is parallel to LP (as now the line PN intersects LP and MN at the same angles and N and P are supplementary angles).
(2)
with the proof in (1) that we have 2 sets of parallel sidelines (LP || MN, LM || PN), this makes LMNP per basic definition a parallelogram.
