Found problems: 2
2014 Purple Comet Problems, 1
The diagram below shows a circle with center $F$. The angles are related with $\angle BFC = 2\angle AFB$, $\angle CFD = 3\angle AFB$, $\angle DFE = 4\angle AFB$, and $\angle EFA = 5\angle AFB$. Find the degree measure of $\angle BFC$.
[asy]
size(4cm);
pen dps = fontsize(10);
defaultpen(dps);
dotfactor=4;
draw(unitcircle);
pair A,B,C,D,E,F;
A=dir(90);
B=dir(66);
C=dir(18);
D=dir(282);
E=dir(210);
F=origin;
dot("$F$",F,NW);
dot("$A$",A,dir(90));
dot("$B$",B,dir(66));
dot("$C$",C,dir(18));
dot("$D$",D,dir(306));
dot("$E$",E,dir(210));
draw(F--E^^F--D^^F--C^^F--B^^F--A);
[/asy]
2014 Contests, 1
The diagram below shows a circle with center $F$. The angles are related with $\angle BFC = 2\angle AFB$, $\angle CFD = 3\angle AFB$, $\angle DFE = 4\angle AFB$, and $\angle EFA = 5\angle AFB$. Find the degree measure of $\angle BFC$.
[asy]
size(4cm);
pen dps = fontsize(10);
defaultpen(dps);
dotfactor=4;
draw(unitcircle);
pair A,B,C,D,E,F;
A=dir(90);
B=dir(66);
C=dir(18);
D=dir(282);
E=dir(210);
F=origin;
dot("$F$",F,NW);
dot("$A$",A,dir(90));
dot("$B$",B,dir(66));
dot("$C$",C,dir(18));
dot("$D$",D,dir(306));
dot("$E$",E,dir(210));
draw(F--E^^F--D^^F--C^^F--B^^F--A);
[/asy]