Step by step
The question
Question: find one interior angle of a regular pentagon.
1 Cut into triangles
A pentagon has 5 sides and 5 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 pentagon into triangles.
Count them: 1, 2, 3.
Each triangle sits on one side of the pentagon, 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: 5 − 2 = 3.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the pentagon.
3 triangles, 180° each: 3 times 180 is 540.
3 Share it out
All 5 angles are the same.
So we share 540° equally: 540/5.
540 divided by 5 is 108.
So each angle is 108°.
4 Check
Let's check: 5 angles of 108° together.
We get 540°, the angle sum.
So 108° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Then: share it out.
Last: check.