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2
Convex pentagon - equality of angles
Convex pentagon - equality of angles
Source:
November 11, 2005
geometry solved
geometry
Problem Statement
A
B
C
D
E
ABCDE
A
BC
D
E
is a convex pentagon such that
D
C
=
D
E
DC = DE
D
C
=
D
E
and
∠
C
=
∠
E
=
9
0
⋅
\angle C = \angle E = 90^{\cdot}
∠
C
=
∠
E
=
9
0
⋅
.
F
F
F
is a point on the side
A
B
AB
A
B
such that
A
F
B
F
=
A
E
B
C
\frac{AF}{BF}= \frac{AE}{BC}
BF
A
F
=
BC
A
E
. Show that
∠
F
C
E
=
∠
A
D
E
\angle FCE = \angle ADE
∠
FCE
=
∠
A
D
E
and
∠
F
E
C
=
∠
B
D
C
\angle FEC = \angle BDC
∠
FEC
=
∠
B
D
C
.
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