I go to sleep at 8pm, wake up at 5.50am the next day, go back to sleep at 6.05am, and wake up for good at 7.01am. How long did I sleep for altogether?

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?

Me find the value of x each figure.

What is the point of inflection for the function f(x)=2cos4x on the interval (0, pi/2)