+4625 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 α below.
+130477
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°) =
(3 /14)(360°)
So 7 times this is
(7)(3/14)(360°) =
(3/2)(360°) = 540°
