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Difference between revisions of "1978 AHSME Problems/Problem 12"

(Undo revision 216641 by Evan the dragon (talk) - vandalism)
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==Problem==
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== Problem ==
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In <math>\triangle ADE</math>, <math>\measuredangle ADE=140^\circ</math>, points <math>B</math> and <math>C</math> lie on sides <math>AD</math> and <math>AE</math>,
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respectively, and points <math>A,~B,~C,~D,~E</math> are distinct.* If lengths <math>AB,~BC,~CD</math>, and <math>DE</math> are all equal,
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then the measure of <math>\measuredangle EAD</math> is
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* The specification that points <math>A,B,C,D,E</math> be distinct was not included in the original statement of the problem.
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If <math>B=D</math>, then <math>C=E</math> and <math>\measuredangle EAD=20^\circ</math>.   
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<math>\textbf{(A) }5^\circ\qquad
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\textbf{(B) }6^\circ\qquad
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\textbf{(C) }7.5^\circ\qquad
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\textbf{(D) }8^\circ\qquad
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\textbf{(E) }10^\circ</math>
  
 
==See Also==
 
==See Also==
 
{{AHSME box|year=1978|num-b=11|num-a=13}}
 
{{AHSME box|year=1978|num-b=11|num-a=13}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 12:34, 16 July 2024

Problem

In $\triangle ADE$, $\measuredangle ADE=140^\circ$, points $B$ and $C$ lie on sides $AD$ and $AE$, respectively, and points $A,~B,~C,~D,~E$ are distinct.* If lengths $AB,~BC,~CD$, and $DE$ are all equal, then the measure of $\measuredangle EAD$ is

  • The specification that points $A,B,C,D,E$ be distinct was not included in the original statement of the problem.

If $B=D$, then $C=E$ and $\measuredangle EAD=20^\circ$.

$\textbf{(A) }5^\circ\qquad \textbf{(B) }6^\circ\qquad \textbf{(C) }7.5^\circ\qquad \textbf{(D) }8^\circ\qquad \textbf{(E) }10^\circ$

See Also

1978 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 11 		Followed by
Problem 13
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
All AHSME Problems and Solutions

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