Interior Angles of a Regular Polygon

As we've seen with the (n-2)180 formula, the sum total of the measures of the interior angles of a polygon can be quickly ascertained. Further, each individual measure within can also be ascertained by dividing the sum total by the actual number of sides (n), as long as the polygon is regular.

As per the image above, the more sides of a regular polygon, the closer the shape comes to being a circle. With that, the interior angles are ever increasing towards a max possible value. So if instead of a decagon drawn inside that circle, I drew a 50-sided shape, it would be near impossible to see the shape inside the circle.

So three questions:

1) What is that max value the interior angle measures are approaching as you increase the number of sides?

2) Give an example of the measure of each interior angle of a (you choose)-sided regular polygon. 

3) What is the sum of the measures of the exterior angles of the polygon you've chosen?

My example for #2:

A 45-sided regular polygon has interior angle measure 172 degrees, because [(n-2)*180]/n gives 172 in my case. 

*You must choose a number that no other student has previously chosen and put into the comment section; shouldn't be a problem, as there are an infinite amount of numbers to choose from, so make sure by looking at the other examples. In addition, the number you choose must be greater than any named or previously discussed polygons. Also, if you can manage to choose a number that gives a whole number value (non-decimal) as the interior angle measure, bonus. First come, first serve with that.*

Contrapositive of a conditional statement

A conditional statement is one which has a hypothesis and a conclusion in the if-then format. So, for example, "If an angle is 45 degrees, then the angle is acute."

The converse of a conditional statement is where you switch the hypothesis and conclusion literally. From the same example, "If the angle is acute, then the angle measures 45 degrees."

Obviously, the converse is a false statement; an acute angle can measure 30 degrees, doesn't have to be 45.

A statement whose converse and original statement are both true statements is a biconditional statement.

My Example: If it is December 25th, then it is Christmas Day.

If it is Christmas Day, then it is December 25th.

Your turn!! (be careful. Make sure it is biconditional!)