Step by step
The question
Question: find the sum of the interior angles of a decagon.
1 Cut into triangles
A decagon has 10 sides and 10 corners.
A polygon is a flat shape with straight sides.
Interior angles are the angles inside, at the corners.
Pick one corner.
Draw lines from it to the other corners.
They cut the decagon into triangles.
Count them: 1, 2, 3, 4, 5, 6, 7, 8.
Each triangle sits on one side of the decagon, away from our corner.
The two sides that touch our corner have no triangle of their own.
So there are 2 fewer triangles than sides: 10 − 2 = 8.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the decagon.
8 triangles, 180° each: 8 × 180.
Forget the zero: 8 times 18 is 144.
Put the zero back: 1440.
Careful: we count the triangles, 8, not the sides, 10.
8 times 180 is 1440.
So the angles add up to 1440°.
3 Check
Let's check: 1440 divided by 180 should give the 8 triangles.
We get 8 triangles.
So 1440° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Last: check.