What is therelation between number of sides and measure of angles in a polygon?
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Answer:
Step-by-step explanation:
What is the relation between the sides and angles of a regular polygon?
What is the relation between the sides and the angles of a regular polygon?
There will be as many angles as the number of sides (n).
Each exterior angle will be equal to 360/n.
Each interior angle will be equal to (180-360/n).
There will be n(n-3)/2 diagonals, all of equal length.
There will be as many congruent isosceles triangles as n.
If n = 6, there will be six congruent equilateral triangles.
The apex angle of each isosceles or equilateral triangle will be the same as the exterior angle.
If n is even, then there will be n/2 rhombuses.
If n is odd, then there will be no rhombuses but n isosceles triangles.
There will be n apothems, all of equal length.
The equal sides of each isosceles or equilateral triangle will be the radius of the circumscribing circle.
The apothem will the radius of the inscribed circle