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Answer :
From the given table, dearly we observe that the sum of angles (interior angles) of a polygon with n sides = \((n – 2)× 180^{\circ}\).
(a) n = 7
Sum of angle =\(\left( 7-2 \right) \times { 180 }^{ \circ }\)
\(= 5\times { 180 }^{ \circ }={ 900 }^{ \circ }\)
∴The sum of angle for 7 sided polygon=\(900^o\)
(b) n = 8
Sum of angles =\( \left( 8-2 \right) \times { 180 }^{ \circ }\)
\(= 6\times { 180 }^{ \circ }={ 1080 }^{ \circ }\)
∴ The sum of the angles of a polygon of 8 sides=\(1080^o\)
(c) n = 10
Angle sum = \(\left( 10-2 \right) \times { 180 }^{ \circ }\)
\(= 8\times { 180 }^{ \circ }={ 1440 }^{ \circ }\)
∴ The sum of the angles of a polygon of 10 sides=\(1440^o\)
(d) We can observe from the given table that the number of triangles is two less them the number of sides in the polygon.
∴ If the polygon has n sides, the number of triangles formed will be (n – 2).
Also we know that the sum of angles of a triangle = \(180^{ \circ }\)
∴ The sum of angles of a polygon of n sides =\( (n – 2) \times180^{ \circ }\)