1958 AHSME Problems/Problem 29

Problem

In a general triangle $ADE$ (as shown) lines $\overline{EB}$ and $\overline{EC}$ are drawn. Which of the following angle relations is true?

[asy] draw((-8,0)--(-2,0)--(4,0)--(10,0)--(0,10)--cycle,dot); draw((-2,0)--(0,10),dot);draw((4,0)--(0,10),dot); MP("A",(-8,0),S);MP("B",(-2,0),S);MP("C",(4,0),S);MP("D",(10,0),S);MP("E",(0,10),N); MP("x",(-7.9,.4),E);MP("z",(-2,.4),W);MP("m",(-2,.4),E);MP("n",(4,.4),W);MP("c",(4,.4),E);MP("a",(9.9,.4),W); MP("y",(-.2,8.8),SW);MP("w",(.1,8.8),S);MP("b",(.7,9),SE); [/asy]

$\textbf{(A)}\ x \plus{} z \equal{} a \plus{} b\qquad \textbf{(B)}\ y \plus{} z \equal{} a \plus{} b\qquad \textbf{(C)}\ m \plus{} x \equal{} w \plus{} n\qquad \\ \textbf{(D)}\ x \plus{} z \plus{} n \equal{} w \plus{} c \plus{} m\qquad \textbf{(E)}\ x \plus{} y \plus{} n \equal{} a \plus{} b \plus{} m$ (Error compiling LaTeX. ! Undefined control sequence.)


Solution

$\fbox{}$

See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 28
Followed by
Problem 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS