for two possible mutually exclusive events a and b, if a does not happens, what is the probability that b happens

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?

Given the two similar triangles, how do i find the missing length? if a=4, b=5, and b'=7.5 find a'

Which property was used to simplify the expression? 3c+9 +4c=3c+4c+9