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National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1978 AMC 12/AHSME
12
12
Part of
1978 AMC 12/AHSME
Problems
(1)
Find <EAD
Source: 1978 AHSME Problem 12
6/6/2014
In
△
A
D
E
\triangle ADE
△
A
D
E
,
∡
A
D
E
=
14
0
∘
\measuredangle ADE=140^\circ
∡
A
D
E
=
14
0
∘
, points
B
B
B
and
C
C
C
lie on sides
A
D
AD
A
D
and
A
E
AE
A
E
, respectively, and points
A
,
B
,
C
,
D
,
E
A,~B,~C,~D,~E
A
,
B
,
C
,
D
,
E
are distinct.* If lengths
A
B
,
B
C
,
C
D
,
AB,~BC,~CD,
A
B
,
BC
,
C
D
,
and
D
E
DE
D
E
are all equal, then the measure of
∡
E
A
D
\measuredangle EAD
∡
E
A
D
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
5
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
6
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
7.
5
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
8
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
1
0
∘
<span class='latex-bold'>(A) </span>5^\circ\qquad<span class='latex-bold'>(B) </span>6^\circ\qquad<span class='latex-bold'>(C) </span>7.5^\circ\qquad<span class='latex-bold'>(D) </span>8^\circ\qquad <span class='latex-bold'>(E) </span>10^\circ
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
5
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
6
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
7.
5
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
8
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
1
0
∘
* The specification that points
A
,
B
,
C
,
D
,
E
A,B,C,D,E
A
,
B
,
C
,
D
,
E
be distinct was not included in the original statement of the problem. If
B
=
D
B=D
B
=
D
, then
C
=
E
C=E
C
=
E
and
∡
E
A
D
=
2
0
∘
\measuredangle EAD=20^\circ
∡
E
A
D
=
2
0
∘
.
AMC