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51.
Explore:
From the figure, you know that
m
/
ABC
5
57 and
m
/
DEF
5
3
x
2
9.
Plan:
For line
p
to be parallel to line
q
,
corresponding angles must be congruent, so
/
ABC
>
/
AED
.Since
/
AED
is supplementary to
/
DEF
, because they are a linear pair, it must be
true that
p
i
q
if
/
ABC
is supplementary to
/
DEF
, or
m
/
ABC
1
m
/
DEF
5
180. Substitute
the given angle measures into this equation and
solve for
x
.
Solve:
m
/
ABC
1
m
/
DEF
5
¬
180
57
1
3
x
2
9
5
¬
180
3
x
5
¬
132
x
5
¬
44
Examine:
Verify the measure of
/
DEF
by using
the value of
x
.That is, 3
x
2
9
5
3(44)
2
9 or 123,
and 57
1
123
5
180. Since
m
/
ABC
1
m
/
DEF
5
180,
m
/
ABC
is supplementary to
/
DEF
, and
p
i
q
.
52. 1.
Given
2.
Subtraction Property
3.
Addition Property
4.
Division Property
53.
any three:
/
2 and
/
11,
/
3 and
/
6,
/
4 and
/
7,
/
3 and
/
12,
/
7 and
/
10,
/
8 and
/
11
54.
/
1 and
/
4,
/
1 and
/
10,
/
5 and
/
2,
/
5 and
/
8,
/
9 and
/
6,
/
9 and
/
12
55.
/
6,
/
9, and
/
12 by alternate interior
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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