How many triangles are in a polygon whose sum of its interior angles is 1080°.
recall that an n-gon's interior angles sum to
(n-2)*180
so, just solve
(n-2)*180 = 1080
The sum of the interior angles of a polygon can be calculated using the formula: (n-2) * 180, where n represents the number of sides (or vertices) of the polygon.
In this case, we have the equation: (n-2) * 180 = 1080.
Let's solve for n:
180n - 360 = 1080
180n = 1440
n = 8
Therefore, the polygon has 8 sides.
A polygon with 8 sides is called an octagon.
To find the number of triangles, we can use the formula: (n-2), where n represents the number of sides.
For the octagon, (8-2) = 6.
Therefore, there are 6 triangles in the polygon.
To determine the number of triangles in a polygon, we need to use the formula:
Number of triangles = (Sum of interior angles - 180°) / 180°
Given that the sum of the interior angles is 1080°, let's substitute the values into the formula:
Number of triangles = (1080° - 180°) / 180°
Number of triangles = 900° / 180°
Number of triangles = 5
Therefore, there are 5 triangles in the polygon whose sum of its interior angles is 1080°.
(n-2)*180 = 1080
180n - 360 = 1080
n = 8
A triangle can be drawn by joining any 3 of the 8 vertices.
that would be C(8,3) or 56 such triangles.