Difference between revisions of "1979 AHSME Problems/Problem 3"
(Created page with "== Problem 3 == <asy> real s=sqrt(3)/2; draw(box((0,0),(1,1))); draw((1+s,0.5)--(1,1)); draw((1+s,0.5)--(1,0)); draw((0,1)--(1+s,0.5)); label("$A$",(1,1),N); label("$B$",(1...") |
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Solution by e_power_pi_times_i | Solution by e_power_pi_times_i | ||
| − | Notice that <math>\measuredangle DAE = 90\circ+60\circ = 150\circ</math> and that <math>AD = AE</math>. Then triangle <math>ADE</math> is isosceles, so <math>\measuredangle AED = \dfrac{180\circ-150\circ}{2} = \boxed{\textbf{(C) } 15}</math>. | + | Notice that <math>\measuredangle DAE = 90^\circ+60^\circ = 150\circ</math> and that <math>AD = AE</math>. Then triangle <math>ADE</math> is isosceles, so <math>\measuredangle AED = \dfrac{180^\circ-150^\circ}{2} = \boxed{\textbf{(C) } 15}</math>. |
== See also == | == See also == | ||
Revision as of 12:27, 3 January 2017
Problem 3
![[asy] real s=sqrt(3)/2; draw(box((0,0),(1,1))); draw((1+s,0.5)--(1,1)); draw((1+s,0.5)--(1,0)); draw((0,1)--(1+s,0.5)); label("$A$",(1,1),N); label("$B$",(1,0),S); label("$C$",(0,0),W); label("$D$",(0,1),W); label("$E$",(1+s,0.5),E); //Credit to TheMaskedMagician for the diagram[/asy]](http://latex.artofproblemsolving.com/4/9/7/4979f48c39324925c22031079f03410ffff35395.png)
In the adjoining figure, 
is a square, 
is an equilateral triangle and point 
is outside square .
What is the measure of 
in degrees?
Solution
Solution by e_power_pi_times_i
Notice that 
and that 
. Then triangle 
is isosceles, so 
.
See also
| 1979 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by num-b=2 |
Followed by Problem 4 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
