Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles

six-pointed-star

#1

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.)

Answer:

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.