The sum of interior angles of a regular polygon is 1080 degrees .What is the number of triangles the polygon can subdivide into
180(n-2) = 1080
n-2 = 6
n = 8
So the polygon has 8 sides and 8 vertices.
Each of the 8 vertices can form a triangle with 2 of the other 7 vertices.
8*6 = 48 triangles can be formed.
But some have been counted twice. How many?
google can provide some insights.
(2n-4)90, when n=6
1080=(2*6-4)90
1080=8*90
1080/72=
To find the number of triangles the polygon can subdivide into, we need to know the formula for calculating the sum of interior angles of a polygon and the relationship between the number of triangles and the number of sides in the polygon.
The formula for the sum of interior angles of a polygon is given by:
Sum = (n - 2) * 180 degrees
where n is the number of sides in the polygon.
Let's substitute the given sum of 1080 degrees into the formula:
1080 = (n - 2) * 180
Now, let's solve for n:
1080 = 180n - 360
1440 = 180n
n = 8
So, the polygon has 8 sides.
To find the number of triangles it can subdivide into, we need to subtract 2 (the 2 triangles that form the ends of the polygon) from the number of sides:
Number of triangles = n - 2 = 8 - 2 = 6
Therefore, the polygon can be subdivided into 6 triangles.
To find the number of triangles the polygon can subdivide into, we need to use the formula for the sum of interior angles of a polygon. The formula is:
Sum of interior angles = (n - 2) * 180 degrees
Where n is the number of sides (or vertices) of the polygon.
In this case, we are given that the sum of interior angles is 1080 degrees. Let's set up the equation to solve for n:
1080 = (n - 2) * 180
To solve for n, we can start by dividing both sides of the equation by 180:
1080 / 180 = n - 2
Simplifying the left side of the equation:
6 = n - 2
Now, let's isolate n by adding 2 to both sides:
6 + 2 = n
8 = n
So, the number of sides (or vertices) of the polygon is 8.
To find the number of triangles the polygon can subdivide into, we can use the fact that each triangle has an interior angle sum of 180 degrees. Since the total sum of interior angles is 1080 degrees, we can divide this by 180:
1080 / 180 = 6
Therefore, the polygon can be subdivided into 6 triangles.