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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1958 AMC 12/AHSME
29
29
Part of
1958 AMC 12/AHSME
Problems
(1)
Relations of Angles in a Triangle
Source:
6/13/2009
In a general triangle
A
D
E
ADE
A
D
E
(as shown) lines
E
B
‾
\overline{EB}
EB
and
E
C
‾
\overline{EC}
EC
are drawn. Which of the following angle relations is true? [asy]defaultpen(linewidth(.8pt)); unitsize(2cm);pair A = origin; pair B = (1,0); pair C = (2,0); pair D = (3,0); pair E = (1.25,1.75);draw(A--D--E--cycle); draw(E--B); draw(E--C);label("
A
A
A
",A,SW); label("
B
B
B
",B,S); label("
C
C
C
",C,S); label("
D
D
D
",D,SE); label("
E
E
E
",E,N); label("
y
y
y
",E,3SW + 3S); label("
w
w
w
",E,7S + E); label("
b
b
b
",E,3SE + 4S + E); label("
x
x
x
",A,NE); label("
z
z
z
",B,NW); label("
m
m
m
",B,NE); label("
n
n
n
",C,NW); label("
c
c
c
",C,NE); label("
a
a
a
",D,NW+W);[/asy]
(A)
\ x \plus{} z \equal{} a \plus{} b\qquad
(B)
\ y \plus{} z \equal{} a \plus{} b\qquad
(C)
\ m \plus{} x \equal{} w \plus{} n\qquad \\
(D)
\ x \plus{} z \plus{} n \equal{} w \plus{} c \plus{} m\qquad
(E)
\ x \plus{} y \plus{} n \equal{} a \plus{} b \plus{} m