2 answers Chaz?

This is what I thought:

Theory 1.

The angle sum of a triangle is 180°
the angle sum of a square is 360°
therefore the angle sum of a pentagon must be 540°


Theory 2.

If triangle is 180° and it has 3 angles ie 60° per angle
and a square is 360° with 4 angles, ie 90° per angle

then a pentagon (5 angles) must have an angle sum of 5 x 120° = 600°

Theory 3.
Lets just say that a triangle is a really bad circle. So bad it only has an angle sum of 180°.
Next is a square, a liitle better in the search for a circle. It has an angle sum of 360°.
Now we know that a circle is perfect and it has 360° in it so its angle sum is 360°. It is a polygon with an infinite number of sides.
By interpolation, the angle sum of a pentagon is 360°

. . .

Any one else got the answer?