Difference between revisions of "1999 AMC 8 Problems/Problem 21"
| Line 9: | Line 9: | ||
label("$110^\circ$",(900/83,-317/83),NNW); | label("$110^\circ$",(900/83,-317/83),NNW); | ||
label("$A$",(0,0),NW); | label("$A$",(0,0),NW); | ||
| − | label("$B$", (20,0), | + | label("$B$", (20,0), NE); |
</asy> | </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 11:57, 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), NE); [/asy]](http://latex.artofproblemsolving.com/f/3/5/f35551ea4d828905a2f3e1d6a2abcc033d9b8d36.png)
Note that 
. So 
.
