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Azerbaijan Junior National Olympiad
2015 Azerbaijan National Olympiad
5
Azerbaijan NMO 2015
Azerbaijan NMO 2015
Source: Azerbaijan NMO 2015
October 21, 2015
geometry
trigonometry
Problem Statement
In the convex quadrilateral
A
B
C
D
ABCD
A
BC
D
angle
∠
B
A
D
=
90
\angle{BAD}=90
∠
B
A
D
=
90
,
∠
B
A
C
=
2
⋅
∠
B
D
C
\angle{BAC}=2\cdot\angle{BDC}
∠
B
A
C
=
2
⋅
∠
B
D
C
and
∠
D
B
A
+
∠
D
C
B
=
180
\angle{DBA}+\angle{DCB}=180
∠
D
B
A
+
∠
D
CB
=
180
. Then find the angle
∠
D
B
A
\angle{DBA}
∠
D
B
A
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