4.5 lj > Answer ExplanationsGeometryACLet A and B be the endpoints of one of the sides
of the hexagon and let C be the center of the
hexagon. Then the degree measure of LACE is
360
—= 60 and the sum of the degree measures of
6
LABCand乙BAGis 180- 60 = 120. Also, since
AC= BC, the degree measures of乙BCand
乙BAGare equal. Therefore, the degree measure of
each of乙1.BCand乙BACis 60. Thus心ABCis an
equilateral triangle with side length AB= 80. It
follows that the length of a diagonal through thecenter of the hexagon is 2(AC) = (^2) ( (^80) ) = 160.
1h e correct answer 1s D.
Q R
p s
U T
PS03695
140.In the figure shown, PQRSTU is a regular polygon with
sides of length x. What is the perimeter of triangle PRT
in terms of x?
Geometry
Since PQRSTU is a regular hexagon, /'::,PQR,
t::,RST, and /'::, TUP are the same size and shape,
so PR= RT= TP and the perimeter of t::,PRTis
3 (PR). Note that in the figure above, PQRSTU
is partitioned into four triangles. The sum of the
degree measures of the interior angles of each
triangle is 180°. The total of the degree measures
of the interior angles of these four triangles is
equal to the sum of the degree measures of the six
interior angles of PQRSTU. Since PQRSTU is a
regular hexagon, each of乙UPQ,乙PQR,乙QRS,
乙RST,乙STU,and乙TUPhas the same measure,
which is (4)(1^80 °) =^120 °.
p
Q
X X
v R
In the figure above, !),_PQR is isosceles with
PQ = QR = x. The measure of乙PQR is 120°,
and the measure of乙P= the measure of
180 °- 120 °
乙R = = 30°. Q V is perpendicular
2
to PR and PV = VR. Since /),_PVQ is a
30 °-60°-90°triangle, its side lengths are in the
x✓
3
ratio 1忑：2,and so PV=——and PR=心3.
2
Therefore, the perimeter of /),_PRT is
3(x✓
3
) = 3x✓
3
.
(A)
x岛
2
(B) x/3
(Cl
3x岛
2
(D) 3x袅
(El 4x岛
1h e correct answer 1s D.
PSll 755
- In a certain medical survey, 45 percent of the people
surveyed had the type A antigen in their blood and 3
percent had both the type (^) A antigen and the type B
antigen. Which of the following is closest to the
percent of those with the type A antigen who also had
the type B antigen?
(A) 1.35%
(B) 6.67%
(C) 13.50%
(D) 15.00%
(E) 42 .00%