1992 AHSME Problems/Problem 20

Problem

$[asy] draw((1,0)--(2*cos(pi/8),2*sin(pi/8))--(cos(pi/4),sin(pi/4))--(2*cos(3*pi/8),2*sin(3*pi/8))--(cos(pi/2),sin(pi/2))--(2*cos(5*pi/8),2*sin(5*pi/8))--(cos(3*pi/4),sin(3*pi/4))--(2*cos(7*pi/8),2*sin(7*pi/8))--(-1,0),black+linewidth(.75)); MP("A_1",(2*cos(5*pi/8),2*sin(5*pi/8)),N);MP("A_2",(2*cos(3*pi/8),2*sin(3*pi/8)),N);MP("A_3",(2*cos(1*pi/8),2*sin(1*pi/8)),N); MP("A_n",(2*cos(7*pi/8),2*sin(7*pi/8)),N); MP("B_1",(cos(4*pi/8),sin(4*pi/8)),S);MP("B_2",(cos(2*pi/8),sin(2*pi/8)),S);MP("B_n",(cos(6*pi/8),sin(6*pi/8)),S); [/asy]$ Part of an "n-pointed regular star" is shown. It is a simple closed polygon in which all $2n$ edges are congruent, angles $A_1,A_2,\cdots,A_n$ are congruent, and angles $B_1,B_2,\cdots,B_n$ are congruent. If the acute angle at $A_1$ is $10^\circ$ less than the acute angle at $B_1$ , then $n=$

$\text{(A) } 12\quad \text{(B) } 18\quad \text{(C) } 24\quad \text{(D) } 36\quad \text{(E) } 60$

Solution

$\fbox{D}$

1992 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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
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1992 AHSME Problems/Problem 20

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