In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? A. (2, -3) B. (5, -3) C. (7, -1) D. (2, -1)

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?

The longer leg of a 30-60-90 trangle is 18

The random variable x is defined as the number marking the sector in which the arrow lands when the spinner in the diagram is spun once.