Difference between revisions of "1999 AMC 8 Problems/Problem 21"
(Created page with "[asy] unitsize(12); draw((0,0)--(20,0)--(1,-10)--(9,5)--(18,-8)--cycle); draw(arc((1,-10),(1+19/sqrt(461),-10+10/sqrt(461)),(25/17,-155/17),CCW)); draw(arc((19/3,0),(19/3-8/17,-1...") |
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| Line 1: | Line 1: | ||
| − | + | <asy> | |
unitsize(12); | unitsize(12); | ||
draw((0,0)--(20,0)--(1,-10)--(9,5)--(18,-8)--cycle); | draw((0,0)--(20,0)--(1,-10)--(9,5)--(18,-8)--cycle); | ||
| Line 5: | Line 5: | ||
draw(arc((19/3,0),(19/3-8/17,-15/17),(22/3,0),CCW)); | draw(arc((19/3,0),(19/3-8/17,-15/17),(22/3,0),CCW)); | ||
draw(arc((900/83,-400/83),(900/83+19/sqrt(461),-400/83+10/sqrt(461)),(900/83 - 9/sqrt(97),-400/83 + 4/sqrt(97)),CCW)); | draw(arc((900/83,-400/83),(900/83+19/sqrt(461),-400/83+10/sqrt(461)),(900/83 - 9/sqrt(97),-400/83 + 4/sqrt(97)),CCW)); | ||
| − | label(rotate(30)*" | + | label(rotate(30)*"$40^\circ$",(2,-8.9),ENE); |
| − | label(" | + | label("$100^\circ$",(21/3,-2/3),SE); |
| − | label(" | + | label("$110^\circ$",(900/83,-317/83),NNW); |
| − | label(" | + | label("$A$",(0,0),NW); |
| − | label(" | + | label("$B$", (20,0), NW); |
| + | </asy> | ||
Note that <math>\angle B=180-100-40=40^\circ</math>. So <math>\angle A=180-110-40=\boxed{30^\circ}</math>. | Note that <math>\angle B=180-100-40=40^\circ</math>. So <math>\angle A=180-110-40=\boxed{30^\circ}</math>. | ||
Revision as of 12:57, 17 June 2011
![[asy] unitsize(12); draw((0,0)--(20,0)--(1,-10)--(9,5)--(18,-8)--cycle); draw(arc((1,-10),(1+19/sqrt(461),-10+10/sqrt(461)),(25/17,-155/17),CCW)); draw(arc((19/3,0),(19/3-8/17,-15/17),(22/3,0),CCW)); draw(arc((900/83,-400/83),(900/83+19/sqrt(461),-400/83+10/sqrt(461)),(900/83 - 9/sqrt(97),-400/83 + 4/sqrt(97)),CCW)); label(rotate(30)*"$40^\circ$",(2,-8.9),ENE); label("$100^\circ$",(21/3,-2/3),SE); label("$110^\circ$",(900/83,-317/83),NNW); label("$A$",(0,0),NW); label("$B$", (20,0), NW); [/asy]](http://latex.artofproblemsolving.com/f/f/1/ff11cc3679b3a023d9131aeb87da30824dc8b7f1.png)
Note that 
. So 
.
