Step by step
The question
Question: find one interior angle of a regular heptagon.
1 Cut into triangles
A heptagon has 7 sides and 7 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 heptagon into triangles.
Count them: 1, 2, 3, 4, 5.
Each triangle sits on one side of the heptagon, 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: 7 − 2 = 5.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the heptagon.
5 triangles, 180° each: 5 times 180 is 900.
3 Share it out
All 7 angles are the same.
So we share 900° equally: 900/7.
900 divided by 7 does not come out even: 128.57 and more digits.
We round it to 128.6.
So each angle is about 128.6°.
4 Check
Let's check: 7 angles of 128.6° together.
We get about 900°, the angle sum.
It is a little off because we rounded.
So about 128.6° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Then: share it out.
Last: check.