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Understanding Angles in Polygons

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Scarlett Edwardes@scarlett_1917
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Ever wondered why a triangle's angles always add up to 180°, or what happens when you add more sides? Understanding polygon angles is actually quite straightforward once you know the two simple rules that work for any shape.
Angles in polygons – page 1

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Sum of Angles in Polygons - The Essential Rules

Here's something brilliant: interior angles in any polygon follow a dead simple formula. Just take the number of sides, subtract 2, then multiply by 180°. So the formula is n−2n-2 × 180° where n equals your sides.

Exterior angles are even easier! They always add up to 360° total, so each one equals 360° ÷ n. Whether you're dealing with a triangle or a dodecagon, these rules never fail.

Let's see this in action with an 8-sided polygon (called an octagon). First, we count our sides - that's 8. Then we subtract 2, giving us 6.

Quick Tip: Remember that exterior angles always total 360° - imagine walking around the outside of any shape and you'll always make one complete turn!

Angles in polygons – page 2

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Working Through the Examples Step-by-Step

Now we multiply that 6 by 180°, which gives us 1080°. That's the total of all interior angles in an octagon - pretty massive compared to a triangle's 180°!

For exterior angles in the same octagon, we use our second rule. Take 360° and divide by 8 sides, giving us 45° for each exterior angle.

The beauty of these formulas is they work every single time. Pentagon? 5−25-2 × 180° = 540°. Hexagon? 6−26-2 × 180° = 720°. You've got this!

Memory Trick: Interior angles get bigger as shapes get more sides, but exterior angles get smaller - they're sharing that same 360° between more corners!

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