help please show me how to slove

Question

The nine-pointed star shown here has a regular nonagon at its center. What is the measure of each angle at the tips of the star to the nearest .1°
?

Answer 1

help please show me how to slove
The nine-pointed star shown here has a regular nonagon at its center. What is the measure of each angle at the tips of the star to the nearest .1°

 

As you know, a nonagon has nine sides.  If you put the nonagon in a 360 degree circle, with each side of the nonagon creating a triangle with the center of the circle.  Dividing the 360 degree circle into nine parts, that is each of these nine  sides create a triangle with the center of the circle with the angle at the circles center being 40 degrees each.  Given a triangle is formed by three angles that sum to 180 degrees, if the angle at the center of the circle is 40 degrees, we know the other two angles at the end of one side of the nonagon sum to 140 degrees ( 70 degrees each).  At any of the corners of the nonagon, we see the angles is comprised of two of these 70 degree angles. 

Hope this helps.  It would be much easier explaining if I could include a picture of what I am describing, but they didn't let you include a picture either.