Question

Look at the angles for all regular polygons. As the number of sides increases, do the measures of the angles increase or decrease? What pattern do you see

Answer 1

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

$x=\frac{(n-2)}{n}(180^o)$

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

$x=\frac{(3-2)}{3}(180^o)=60^o$

A square

n=4 sides

$x=\frac{(4-2)}{4}(180^o)=90^o$

A pentagon

n=5 sides

$x=\frac{(5-2)}{5}(180^o)=108^o$

A hexagon

n=6 sides

$x=\frac{(6-2)}{6}(180^o)=120^o$

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 $x=\frac{(n-2)}{n}(180^o)$