Sat math Essentials

5.
c.
Since 
AB
and 
CD
are parallel lines cut by trans-
versals 
EF
and 
GH
respectively, angles 
CKG
and
IJK
are alternating angles. Alternating angles
are equal in measure, so angle 
IJK
= 55 degrees.
Angles 
EIJ
and 
JIK
form a line. They are sup-
plementary and their measures sum to 180
degrees. Angle 
JIK
= 180 – 140 = 40 degrees.
Angles 
JIK
,
IJK
, and 
IKJ
comprise a triangle.
There are 180 degrees in a triangle; therefore, the
measure of angle 
IKJ
= 180 – (55 + 40) = 85
degrees.
6.
d.
There are three numbers on the cube that are
even (2, 4, 6), so the probability of rolling an
even number is 
1
2
. There are two numbers on the
cube that are factors of 9 (1, 3), so the proba-
bility of rolling a factor of 9 is 
2
6
or 
1
3
. No num-
bers are members of both sets, so to find the
probability of rolling either a number that is
even or a number that is a factor of 9, add the
probability of each event:
1
2
+ 
1
3
= 
3
6
+ 
2
6
= 
5
6
.
7.
d.
The area of a square is equal to the length of
a side, or edge, of the square times itself. If
the area of a square face is 121 square units,
then the lengths of two edges of the prism
are 11 units. The volume of the prism is 968
cubic units. The volume of prism is equal to
lwh
, where 
l
is the length of the prism,
w
is
the width of the prism, and 
h
is the height of
the prism. The length and width of the prism
are both 11 units. The height is equal to: 968
= (11)(11)
h
, 968 = 121
h
,
h
= 8. The prism
has two square faces and four rectangular
faces. The area of one square face is 121
square units. The area of one rectangular
face is (8)(11) = 88 square units. Therefore,
the total surface area of the prism is equal to:
2(121) + 4(88) = 242 + 352 = 594 square
units.