The angles marked in this figure are in units of 180/7°. So the internal angles in a heptagon will add up to 35, the internal angles in a pentagon will add up to 21, in a quadrilateral will sum to 14 , and in a triangle or on a line will sum to 7.

By definition all of the angles in the regular heptagon will be 5. From pentagon NBCDE, angle ENB is 1 (same for angle GPD).

Since H and K are midpoints of the heptagon, FGHK is a trapezoid, therefore HK is parallel to GF, and so angle HKE is 5 (same for JLD). The supplementary angles MKN and MLP are therefore 2.

From the inherent symmetry of the figure, and the angles in the quadrilateral NPDE, angles ENP and DPN are each 2. Therefore from triangle NMK, angle NMK is 3 (same for PML). From the pentagon MKEDL, angle KML is 1.

Finally, since NMK is isosceles, NM = MK (same for MP). So if MK is 7, NP = 14.