Louis bought a laptop for
$720. It was marked $90
off because it was an
opened product. He also
got a 15% discount, which
was taken off the original
price. What was the
original price of the laptop?

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?

Solve the system of equations using the linear combination method. {4x−3y=127x−3y=3 enter your answers in the boxes.

What is the measure of each of the two angles formed by the bisector of the diagonal of a rhombus if the original angle measures 58 degrees?