17. a. The measure of an exterior angle of a triangle is
equal to the sum of the two interior angles of the
triangle to which the exterior angle is NOT sup-
plementary. Angle
i is supplementary to angle
g ,
so the sum of the interior angles
e and
f is equal
to the measure of angle
i :
i =
e +
f .
18. e. An irrational number is a number that cannot
be expressed as a repeating or terminating dec-
imal. (
32
)
3
= (
32
)(
32
)(
32
) = 32
32
= 32
16
2
= (32)(4)
2
= 128
2
.
2
can-
not be expressed as a repeating or terminating
decimal, therefore, 128
2
is an irrational
number.
19. b. The area of a square is equal to
s 2
, where
s is the
length of a side of the square. The area of
ABCD is 4
2
= 16 square units. The area of a circle is
equal to
π
r 2
, where
r is the radius of the circle.
The diameter of the circle is four units. The
radius of the circle is
4
2
= two square units. The
area of the circle is equal to
π
(2)
2
= 4
π
. The
shaded area is equal to one-fourth of the differ-
ence between the area of the square and the area
of the circle:
1
4
(16 – 4
π
) = 4 –
π
.
20. a. To increase
d by 50%, multiply
d by 1.5:
d = 1.5
d .
To find 50% of 1.5
d , multiply 1.5
d by 0.5:
(1.5
d )(0.5) = 0.75
d . Compared to its original
value,
d is now 75% of what it was. The value of
d is now 25% smaller.
