Question

find the number of sides in a polygon if the sum of its interior angles is 1260°?

Answer 1

Given :

• Interior angles is 1260°

To find :

• Number of sides in a polygon

Solution :

Let ,

N be the sum sides of a polygon .

Then , the sum of its interior Angeles .

= ( 2n - 4 ) Right angle

= [( 2n - 4 )× 90]°

Therefore ,

( 2n - 4 ) × 90° = 1260°

$=2n - 4 = \frac{1260°}{90°} = 14$

2n = 18

n = 9

Hence , the number of sides of the given polygon = 9

Answer 2

Concept used

~Here the concept of interior angle sum property is used. The sum of interior angle is given as 1260°. By apply the formula of interior angle sum property of polygon we will get the number of sides.

Formula used

$» \bold\red{(2n-4)×90°}$

• n denotes the number of sides

Solution

♦ We know, sum of angles in a polygon is given as (2n-4)×90°

and also,

Given sum = 1260°

$\sf{\implies 1260= (2n-4)×90°} \\ \\ \sf{\implies \frac{1260}{90}= (2n-4)} \\ \\ \sf{ \implies 14 = 2n-4}$

By transposing the terms, we get

$\sf{\implies 14+4 = 2n}\\ \\ \sf{\implies 18 = 2n}\\ \\ \sf{\implies \frac{18}{2} = n}\\ \\ \sf{\implies \color{purple}n= 9}$

Therfore the polygon has 9 sides.

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More to know !!

Polygon is defined as a simple closed curve made up of line segment.

Classification of Polygons on the basis of sides.

⌬ 3 sides - tríangle

⌬ 4 sides - Quadrilateral

⌬ 5 sides - pentagon

⌬ 6 sides - hexagon

⌬ 7 sides - heptagon

⌬ 8 sides - octagon

⌬ 9 sides - Nonagon

⌬ 10 sides - Decagon

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