What are the peoperties of polygons?
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Hi friend,
Properties of a polygon are:
1.)The number of sides of the shape.
2.)The angles between the sides of the shape.
3.)The length of the sides of the shape.
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Properties of a polygon are:
1.)The number of sides of the shape.
2.)The angles between the sides of the shape.
3.)The length of the sides of the shape.
Hope it helps. Please mark as brainliest.
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Answered by
1
Properties of Polygon:
1. A polygon with n sides, have as their sum of their interior angles 180 ° (n-2)
Reference is made to any vertex and triangles (n - 2) are drawn in the polygon.
The sum of the angles of a triangle is 180 °.
It is easy to see that the sum of the inner angles of the polygon is the sum of the angles of the triangles.
A + B + C + D + E = 190 ° (n-2)
If the polygon is regular, and it is desired to calculate the value of the interior angle, it is enough to divide 180 ° (n - 2) between the number of sides of the polygon.
Interior Angle => (n-2) x 180°/n
2. The sum of the exterior angles of a polygon is equal to 360 °
The sum of the inner and outer angles of a vertex of the polygon is 180 °.
The sum of the inner and outer angles of the polygons is 180 ° n.
Therefore, at 180 ° n we subtract the sum of the interior angles 180 ° (n - 2).
180 ° n - 180 ° (n - n + 2) = 360 °
Sum of external angles = 360 °
3. The total of diagonals that can be drawn in a polygon of n sides, is obtained with the expression D = n ( n-3)/2
(n - 3) are the diagonals that can be drawn from each vertex because there will always be three vertices that can not be diagonally plotted, the vertex from which it is drawn and the two contiguous ones.
Each diagonal touches two vertices, then double counts each diagonal therefore:
Number of diagonals = D = n (n-3)/2
1. A polygon with n sides, have as their sum of their interior angles 180 ° (n-2)
Reference is made to any vertex and triangles (n - 2) are drawn in the polygon.
The sum of the angles of a triangle is 180 °.
It is easy to see that the sum of the inner angles of the polygon is the sum of the angles of the triangles.
A + B + C + D + E = 190 ° (n-2)
If the polygon is regular, and it is desired to calculate the value of the interior angle, it is enough to divide 180 ° (n - 2) between the number of sides of the polygon.
Interior Angle => (n-2) x 180°/n
2. The sum of the exterior angles of a polygon is equal to 360 °
The sum of the inner and outer angles of a vertex of the polygon is 180 °.
The sum of the inner and outer angles of the polygons is 180 ° n.
Therefore, at 180 ° n we subtract the sum of the interior angles 180 ° (n - 2).
180 ° n - 180 ° (n - n + 2) = 360 °
Sum of external angles = 360 °
3. The total of diagonals that can be drawn in a polygon of n sides, is obtained with the expression D = n ( n-3)/2
(n - 3) are the diagonals that can be drawn from each vertex because there will always be three vertices that can not be diagonally plotted, the vertex from which it is drawn and the two contiguous ones.
Each diagonal touches two vertices, then double counts each diagonal therefore:
Number of diagonals = D = n (n-3)/2
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