Question

I know the equation for limits, but how do I find a limit for the measurement of one interior angle in a regular polygon?

Answer 1

the total of all the angles of a N sided polygon is = (N-2)*180

Answer 2

So one of the interior angles will be?

Answer 3

What do you mean one of the interior angles will be?

Answer 4

I'm not exactly sure what you mean

Answer 5

one interior angle of a polygon will be

\[\frac{ (N-2)*180 }{ N }\]

Answer 6

Where N is the number of sides

Answer 7

right my equation my teacher gave me is \[\frac{y= 180x-360 }{ x } \]

Answer 8

I'm using a graph for this equation

Answer 9

ok, so what is the question?

Answer 10

How do I use this equation to find the limit of the measure of one interior angle in a regular polygon?

Answer 11

Does it matter what I use for x?

Answer 12

You want the limit as the number of sides goes to infinity?

Answer 13

Yes, exactly.

Answer 14

right, well think about it, if you keep adding more and more sides, each angle is going to approach a straight line, but not quite

Answer 15

Right...

Answer 16

so this is the equation

Answer 17

Is there an actual number that can be achieved?

Answer 18

\[\lim_{x \rightarrow \infty} [ 180 - \frac{ 360 }{ x }]\]

Answer 19

As x gets very large, the fraction 360/x gets very small and approaches zero

Answer 20

The limit would be 180

Answer 21

Graph: y = 180 - 360/x

look at what y approaches as you look at huge x values.

Answer 22

But how does y get to 180 if it keeps getting smaller and smaller?

Answer 23

Is there a specific number that can be achieved for y that I can physically write down?