Step by step
The question
Question: find the sum of the interior angles of a quadrilateral.
1 Cut into triangles
A quadrilateral has 4 sides and 4 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 quadrilateral into triangles.
Count them: 1, 2.
Each triangle sits on one side of the quadrilateral, 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: 4 − 2 = 2.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the quadrilateral.
2 triangles, 180° each: 2 × 180.
Careful: we count the triangles, 2, not the sides, 4.
2 times 180 is 360.
So the angles add up to 360°.
3 Check
Let's check: add the 2 triangles one by one.
We get 360° again.
So the sum is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Last: check.