Difference between revisions of "2014 AMC 8 Problems/Problem 15"
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− | + | The circumference of the circle with center <math>O</math> is divided into <math>12</math> equal arcs, marked the letters <math>A</math> through <math>L</math> as seen below. What is the number of degrees in the sum of the angles <math>x</math> and <math>y</math>? | |
+ | |||
+ | <asy> | ||
+ | size(230); | ||
+ | defaultpen(linewidth(0.65)); | ||
+ | pair O=origin; | ||
+ | pair[] circum = new pair[12]; | ||
+ | string[] let = {"$A$","$B$","$C$","$D$","$E$","$F$","$G$","$H$","$I$","$J$","$K$","$L$"}; | ||
+ | draw(unitcircle); | ||
+ | for(int i=0;i<=11;i=i+1) | ||
+ | { | ||
+ | circum[i]=dir(120-30*i); | ||
+ | dot(circum[i],linewidth(2.5)); | ||
+ | label(let[i],circum[i],2*dir(circum[i])); | ||
+ | } | ||
+ | draw(O--circum[4]--circum[0]--circum[6]--circum[8]--cycle); | ||
+ | label("$x$",circum[0],2.75*(dir(circum[0]--circum[4])+dir(circum[0]--circum[6]))); | ||
+ | label("$y$",circum[6],1.75*(dir(circum[6]--circum[0])+dir(circum[6]--circum[8]))); | ||
+ | label("$O$",O,dir(60)); | ||
+ | </asy> | ||
+ | |||
+ | <math> \textbf{(A) }75\qquad\textbf{(B) }80\qquad\textbf{(C) }90\qquad\textbf{(D) }120\qquad\textbf{(E) }150 </math> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=14|num-a=16}} | {{AMC8 box|year=2014|num-b=14|num-a=16}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 18:45, 26 November 2014
The circumference of the circle with center is divided into equal arcs, marked the letters through as seen below. What is the number of degrees in the sum of the angles and ?
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.