Determine the measure of the angle in each point of the six-pointed star appearing on
police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following
theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that cuts off the same arc. See the figure.)
by using the above stated theorem,let the angle at the point be \theta ,so the angle making from centre to the opposite two points of the star wiil be 2*\theta. from the triangle formed (\theta + \theta/2 + \theta/2)=180 ; from this \theta=60.