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.
Notice, tertre, that inscribed angle ACE intercepts minor arc AE which measures (3/7) of the circumference of the circle = (3/7)(360° )
So.....the measure of ACE = measure of α = (1/2) of its intercepted arc =
(1/2)* (3/7) (360°) =
So 7 times this is
(3/2)(360°) = 540°