Question

The sum of the interior angle of a regular polygon is 1260
Find the number of sides of the polygon.

Answer 1

sum of interior angles =(n - 2)×180

Given → sum of interior angles = 1260

sum of interior angles = (n-2) ×180

→ 1260=(n-2) ×180

→ 1260/180 = n -2

→ 7 = n-2

→ 7+2= n

→ n = 9

the no. of sides of polygon = 9 sides ( nonagon)

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Answer 2

Given :

• The sum of the interior angle of a regular polygon is 1260⁰

To find :

• The number of sides of the polygon.

Solution :

Let , n be a number of sides of a polygon .

then the sum of interior angles is

= ( 2n - 4 ) right angle

= [ 2n - 4 × 90] ⁰

∴ ( 2n - 4 ) × 90⁰ = 1260⁰

$\red{\sf⟹} \:\sf 2n - 4 = \frac{1260⁰}{90⁰} = 14$

2n = 18

n = 9

the number of sides of polygon is 9