MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2006 National Olympiad First Round
33
33
Part of
2006 National Olympiad First Round
Problems
(1)
Turkey NMO 2006 1st Round - P33 (Geometry)
Source:
2/3/2013
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrileteral such that
m
(
A
B
D
^
)
=
4
0
∘
m(\widehat{ABD})=40^\circ
m
(
A
B
D
)
=
4
0
∘
,
m
(
D
B
C
^
)
=
7
0
∘
m(\widehat{DBC})=70^\circ
m
(
D
BC
)
=
7
0
∘
,
m
(
B
D
A
^
)
=
8
0
∘
m(\widehat{BDA})=80^\circ
m
(
B
D
A
)
=
8
0
∘
, and
m
(
B
D
C
^
)
=
5
0
∘
m(\widehat{BDC})=50^\circ
m
(
B
D
C
)
=
5
0
∘
. What is
m
(
C
A
D
^
)
m(\widehat{CAD})
m
(
C
A
D
)
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
2
5
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
3
0
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
3
5
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
3
8
∘
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
4
0
∘
<span class='latex-bold'>(A)</span>\ 25^\circ \qquad<span class='latex-bold'>(B)</span>\ 30^\circ \qquad<span class='latex-bold'>(C)</span>\ 35^\circ \qquad<span class='latex-bold'>(D)</span>\ 38^\circ \qquad<span class='latex-bold'>(E)</span>\ 40^\circ
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
2
5
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
3
0
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
3
5
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
8
∘
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
4
0
∘
geometry
angle bisector