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Polygons

The Hook

Many-sided figures.

What is it?

Closed 2D shapes with straight sides (Pentagon, Hexagon, Octagon).

Time Travel (History)

Archimedes approximated Pi by drawing polygons with 96 sides!

Cheat Code

Sum of angles = (Sides - 2) * 180.

Practice This Now!

The Field Guide

In Plain English: Poly means 'Many', Gon means 'Angle'. A polygon is just a shape with straight lines. The more sides it has, the more it looks like a circle. We name them by number: 5=Penta, 6=Hexa, 8=Octa.

In The Real World: Stop Signs (Octagon). Honeycombs (Hexagon - the most efficient shape for packing).

How To Do It

  1. Count the number of sides (n).
  2. Subtract 2 (this tells you how many triangles fit inside).
  3. Multiply by 180.
  4. Result is the total sum of all interior angles.
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Booby Trap!

Counting corners wrong. An n-gon has n sides and n corners.

Real World Challenge
"What is the sum of angles in a Stop Sign (Octagon)?"
The Logic: Octagon has 8 sides. (8 - 2) = 6. 6 * 180 = 1080 degrees total.

Training Drills

Formula
(n-2)180
n = side count.