Step by step
The question
Question: find the sum of the interior angles of a polygon with 9 sides.
1 Cut into triangles
A polygon with 9 sides has 9 sides and 9 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 polygon into triangles.
Count them: 1, 2, 3, 4, 5, 6, 7.
Each triangle sits on one side of the polygon, 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: 9 − 2 = 7.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the polygon.
7 triangles, 180° each: 7 × 180.
Forget the zero: 7 times 18 is 126.
Put the zero back: 1260.
Careful: we count the triangles, 7, not the sides, 9.
7 times 180 is 1260.
So the angles add up to 1260°.
3 Check
Let's check: 1260 divided by 180 should give the 7 triangles.
We get 7 triangles.
So 1260° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Last: check.