Need help with this, will mark brainliest (Already did DNE, not correct)

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Find all the values of x that make 0.1x + 0.25(102 - x) < 17.10 true.

Me, prove a quadrilateral with vertices g(1,-1), h(5,1), i(4,3) and j(0,1) is a rectangle using the parallelogram method and a rectangle method.