The right triangle at the top and the one on the right are congruent—they
have the same hypotenuse and the same longer leg—so the two
unknown angles in the upper right are equal:And now that you know the other two angles in that triangle with y, youcan solve for y :Therefore, y – x = 75 – 15 = 60.41 . A
Think of the original statement as “If p, then q,” in which p is “x is a
member of set S,” and q is “x is not a member of set T.” “If p, then q” is
equivalent to “If not q, then not p,” or “If x is a member of set T, then x is
not a member of set S.” That’s statement I. Statement II does not follow
because it’s “If q, then p,” and statement III does not follow because it’s
“If not p, then not q.”
42 . D
The perimeter of triangle ABC is 20. One side is given as 4, so the other
two sides add up to 16. The three sides cannot be 4, 4, and 12, because
that violates the Triangle Inequality Theorem. The sides must be 4, 8, and
8: