Tiki, Alan, and Hans sent a total of 102 text messages during the weekend. Hans sent 2 times as many messages as Alan. Tiki sent 6 more messages than Alan. How many messages did they each send ?

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?

Natasha spent 1 1/2 hours on the beach. she fell asleep for 3/4 of the time she was on the beach and then woke up with a terrible sunburn.how many hours was natasha asleep on the beach?

Listed in the table is the percentage of students who chose each kind of juice at lunchtime. use the table to determine the measure of the central angle you would draw to represent orange juice in a circle graph