Step by step
The question
Question: find one interior angle of a regular dodecagon.
1 Cut into triangles
A dodecagon has 12 sides and 12 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 dodecagon into 10 triangles.
Each triangle sits on one side of the dodecagon, 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: 12 − 2 = 10.
2 Add the triangles
The angles in each triangle add up to 180°.
Together, the triangles make all the angles of the dodecagon.
10 triangles, 180° each: 10 times 180 is 1800.
Forget the zero: 10 times 18 is 180.
Put the zero back: 1800.
3 Share it out
All 12 angles are the same.
So we share 1800° equally: 1800/12.
1800 divided by 12 is 150.
So each angle is 150°.
4 Check
Let's check: 12 angles of 150° together.
We get 1800°, the angle sum.
So 150° is right!
Let's look back.
First: cut into triangles.
Then: add the triangles.
Then: share it out.
Last: check.