The polygon angle sum theorem states that the sum of the measures of the interior angles of an n-gon is (n-2) 180
What is a polygon or an n-gon?
A polygon is a geometric figure with a finite number of sides in 2D. A polygon's sides are made up of straight-line segments. They are called as sides. The intersection of two line segments is known as the vertex and an angle is generated as result.
The term n-gon refers to polygon with n sides.
What are the interior angles of a Polygon or an n-gon?
A polygon's interior angle is the angle formed between two adjacent sides of the polygon.
How to find the sum of the measures of the interior angles of an n-gon?
We will take a pentagon(5 sides) and then we will try to generalize it to an n-gon(n sides) with the following steps:
- In the figure let's take the vertex B and connect all the other vertices to it.
- Now, look there are a total of 3 triangles formed inside the pentagon.
- So, now we can say if we add connect all the vertices of an n-gon from a random vertex it will produce a total of (n-2) triangles in it.
What is the sum of the interior angles of a triangle?
The sum of the interior angles of a triangle is 180°
Now, each triangle has the sum of interior angles of 180°,
so (n-2) triangles will have the sum of interior angles of (n-2)×180°.
Therefore, the sum of the measures of the interior angles of an n-gon is (n-2)×180.
Learn more about polygons and their interior angles here -brainly.com/question/1592456
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