a rhombus is a parallelogram with a pair of opposite equal acute angles, a pair of opposite equal obtuse angles, and four equal sides.
in other words, it is a parallelogram with 4 equal sides, including a square as a special case.
the diagonal intersection point is the midpoint of both diagonals.
the diagonals intersect each other at a right angle (90°).
and they split each vertex angle in half.
so, they split the whole rhombus into 4 equal right-angled triangles.
and remember, the sum of all angles in a triangle is always 180°.
an "obtuse" angle means an angle larger than 90°.
an "acute" angle means an angle smaller than 90°.
because of all that, in the triangle PKE the angle K must be greater than 45° (90/2 = 45), so that the rhombus angle K can be "obtuse", as it must be twice the triangle angle K.
the triangle angle E is 90°.
so, the 16° must be triangle angle P.
and the triangle angle K is then
triangle angle K = 180 - 90 - 16 = 74°.
so, rhombus angle K = rhombus angle N = 2×74 = 148°
and triangle PMN angle N = 74°.
triangle PMN angle M = triangle PMN angle P = 16°.