Step by step
The question
Question: find one interior angle of a regular 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.
Regular means all the sides are equal, and all the angles are equal.
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 times 180 is 1440.
Forget the zero: 8 times 18 is 144.
Put the zero back: 1440.
3 Share it out
All 10 angles are the same.
So we share 1440° equally: 1440/10.
1440 divided by 10 is 144.
So each angle is 144°.
4 Check
Let's check: 10 angles of 144° together.
We get 1440°, the angle sum.
So 144° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Then: share it out.
Last: check.