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All-Russian Olympiad
1987 All Soviet Union Mathematical Olympiad
450
450
Part of
1987 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 450 All Soviet Union MO 198equal angles, given and wanted in convex pentagon
Source:
8/7/2019
Given a convex pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
with
∠
A
B
C
=
∠
A
D
E
\angle ABC= \angle ADE
∠
A
BC
=
∠
A
D
E
and
∠
A
E
C
=
∠
A
D
B
\angle AEC= \angle ADB
∠
A
EC
=
∠
A
D
B
. Prove that
∠
B
A
C
=
∠
D
A
E
\angle BAC = \angle DAE
∠
B
A
C
=
∠
D
A
E
.
geometry
pentagon
equal angles