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# 4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n

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 =$$(n – 2) \times180^{ \circ }$$