Answer:
Yes, i believe that the generalization about the measure of a point angle of a star polygon is true.
First we find sum of interior angle of an n-sided star polygon.
number of triangle in a polygon = n - 2
sum of interior angle of a triangle = 180°
sum of interior angle of an n-sided star polygon = ( n - 2 ) × 180°
To find measure of a point angle, we use:
[tex]\frac{|n-2(d)|}{n}[/tex] × 180°
To find a point angle we eliminate density by multiplying d by 2 in the formula for finding number of triangle, divide the whole by total number of sides and then multiply by the sum of interior angle of triangle(180°).
Since all the angle of a regular star polygon are equal, we can calculate each pointy interior angle of a regular star polygon using the formula given below:
[tex]\frac{|n-2(d)|}{n}[/tex] × 180°
