Task 657

The task

Seven points are evenly spaced out on a circle and connected as shown below to form a 7-pointed star. What is the sum of the angle measurements of the seven tips of the star, in degrees? One such angle is marked as $\alpha$ below. [asy] dotfactor=4; draw(Circle((0,0),1)); real x = 2*pi/7; pair A,B,C,D,E,F,G; A=(cos(4*x), sin(4*x)); B=(cos(3*x), sin(3*x)); C=(cos(2*x), sin(2*x)); D=(cos(x), sin(x)); E=(cos(5*x), sin(5*x)); F=(cos(6*x), sin(6*x)); G=(cos(7*x), sin(7*x)); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(G); dot((0,0)); label("$A$",A,W); label("$B$",B,W); label("$C$",C,N); label("$D$",D,N); label("$E$",G,ENE); label("$F$",F,SE); label("$G$",E,S); draw(A--C--G--E--B--D--F--cycle); label("$\alpha$",C, - 1.5*dir(C)); [/asy]