Use the diagram below to find the lengths of the missing sides. Figures in each diagram are similar. X=15
X=10
X=40
X=30

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?

Which of the greatest common gcf of 32 and 48 a 16 b 96 c 8 d 32

Noor brought 21 sheets of stickers. she gave 1/3 of a sheet to each of the 45 students at recess. she wants to give teachers 1 1/2 sheets each.