Step by step
The question
Question: find one interior angle of a regular octagon.
1 Cut into triangles
An octagon has 8 sides and 8 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 octagon into triangles.
Count them: 1, 2, 3, 4, 5, 6.
Each triangle sits on one side of the octagon, 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: 8 − 2 = 6.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the octagon.
6 triangles, 180° each: 6 times 180 is 1080.
Forget the zero: 6 times 18 is 108.
Put the zero back: 1080.
3 Share it out
All 8 angles are the same.
So we share 1080° equally: 1080/8.
1080 divided by 8 is 135.
So each angle is 135°.
4 Check
Let's check: 8 angles of 135° together.
We get 1080°, the angle sum.
So 135° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Then: share it out.
Last: check.