Answer:
As the number of sides increases, the measures of the angles increase
see the explanation
Step-by-step explanation:
we know that
The measure of the interior angle in a regular polygon is equal to
[tex]x=\frac{(n-2)}{n}(180^o)[/tex]
where
n is the number of sides of the regular polygon
x is the measure of the interior angle in a regular polygon
we have that
Examples
A triangle
n=3 sides
[tex]x=\frac{(3-2)}{3}(180^o)=60^o[/tex]
A square
n=4 sides
[tex]x=\frac{(4-2)}{4}(180^o)=90^o[/tex]
A pentagon
n=5 sides
[tex]x=\frac{(5-2)}{5}(180^o)=108^o[/tex]
A hexagon
n=6 sides
[tex]x=\frac{(6-2)}{6}(180^o)=120^o[/tex]
so
n ----> 3,4,5,6...
x ----> 60°,90°,108°,120°,...
As the number of sides increases, the measures of the angles increase
The pattern is [tex]x=\frac{(n-2)}{n}(180^o)[/tex]
