Pentagon inscribed in circle; find angle
Source: AMC 10 2011 b Problem 17
February 25, 2011
ratiogeometrytrapezoidAMC
Problem Statement
In the given circle, the diameter is parallel to , and is parallel to . The angles and are in the ratio . What is the degree measure of angle ? [asy]
unitsize(7mm);
defaultpen(linewidth(.8pt)+fontsize(10pt));
dotfactor=4;
real r=3;
pair A=(-3cos(80),-3sin(80));
pair D=(3cos(80),3sin(80)), C=(-3cos(80),3sin(80));
pair O=(0,0), E=(-3,0), B=(3,0);
path outer=Circle(O,r);
draw(outer);
draw(E--B);
draw(E--A);
draw(B--A);
draw(E--D);
draw(C--D);
draw(B--C);
pair[] ps={A,B,C,D,E,O};
dot(ps);
label("",A,N);
label("",B,NE);
label("",C,S);
label("",D,S);
label("",E,NW);
label("$$",O,N);[/asy]
$ (A)\ 120 \qquad
(B)\ 125 \qquad
(C)\ 130 \qquad
(D)\ 135 \qquad
(E)\ 140 $