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National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1994 AMC 12/AHSME
9
9
Part of
1994 AMC 12/AHSME
Problems
(1)
1994 AMC 12 #9
Source:
12/30/2011
If
∠
A
\angle A
∠
A
is four times
∠
B
\angle B
∠
B
, and the complement of
∠
B
\angle B
∠
B
is four times the complement of
∠
A
\angle A
∠
A
, then
∠
B
=
\angle B=
∠
B
=
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1
0
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
1
2
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1
5
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1
8
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
22.
5
∘
<span class='latex-bold'>(A)</span>\ 10^{\circ} \qquad<span class='latex-bold'>(B)</span>\ 12^{\circ} \qquad<span class='latex-bold'>(C)</span>\ 15^{\circ} \qquad<span class='latex-bold'>(D)</span>\ 18^{\circ} \qquad<span class='latex-bold'>(E)</span>\ 22.5^{\circ}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
1
0
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
2
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
1
5
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
1
8
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
22.
5
∘
AMC