This document discusses properties of polygons, including: 1) The sum of interior angles in a triangle is 180 degrees, and the sum of interior angles in an n-sided polygon is (n-2) x 180 degrees. 2) The sum of angles can be 900 degrees for a heptagon/septagon with 7 sides, but cannot be 1600 degrees as that number of degrees does not correspond to a whole number of sides. 3) The sum of outer angles (exterior angles) of any polygon is always 360 degrees, with the outer angles at each vertex summing to 180 degrees.

1. Polygons

2. 2

3. Sumofangles
3

4. Quadrilateral
Pentagon
180
o 180
o
180o 180o
180o
2 x 180o = 360o
3
4 sides
5 sides
3 x 180
o
= 540
o
Hexagon6 sides
180o 180o
180o
180o
4 x 180o = 720o
4
Heptagon/Septagon7 sides
180o
180o
180o
180o
180o
5 x 180o = 900o
5
2
1 diagonal
2 diagonals
3 diagonals
4 diagonalsTGES Polygons Dipali G.

5. Polygon
Polygon is a closed figure with
three or more sides..
• Sum of the interior angles of a triangle is
180 0.
• The sum of the angles of an n-sided Polygon
is (n-2)x 180 0
5

6. Is the sum of the angles of any polygon is
16000
? 𝐻𝑜𝑤 𝑎𝑏𝑜𝑢𝑡 9000
?
Let Sum of the angles of the
polygon=16000
n=8.89+2=10.89
n is not a multiple of 180
Therefore ,16000 cannot be the sum of the
angles of a polygon.
6

7. 𝐻𝑜𝑤 𝑎𝑏𝑜𝑢𝑡 9000
?
n=5+2=7
Therefore 900 can be the sum of the interior angles.
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8. Outer Angle
8
Outer angle is the angle
between a side of a
polygon and an
extended adjacent side
of the polygon
Inner angle and
outer angle at a
vertex of a polygon
form a linear pair.
• The exterior
angle(outer angle) at
each vertex of a
polygon can be
determined by
subtracting the
interior angle of each
vertex from 1800.

9. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
9

10. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
3x180=540
10

11. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
3x180=540 180
11

12. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
3x180=540 180 540-180=360
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13. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
3x180=540 180 540-180=360
4x180=720 2x180=360 720-360=360
13

14. Outer Angle(Exterior angle)
Polygon Sum of inner angle + sum of
outer angle
Sum of inner angle Sum of outer angle
3x180=540 180 540-180=360
4x180=720 2x180=360 720-360=360
6x180=1080 4x180=720 1080-720=360
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15. Sum of outer angle
(Exterior angle) of any
polygon is 3600
For any polygon, the two
outer angles at the same
vertex are equal
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16. Thank
You