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

2 thoughts on “find the number of sides in a polygon if the sum of its interior angles is 1260°?”

1. 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

   [tex]» \bold\red{(2n-4)×90°}[/tex]

   • 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°

   [tex] \sf{\implies 1260= (2n-4)×90°} \\ \\ \sf{\implies \frac{1260}{90}= (2n-4)} \\ \\ \sf{ \implies 14 = 2n-4}[/tex]

   By transposing the terms, we get

   [tex] \sf{\implies 14+4 = 2n}\\ \\ \sf{\implies 18 = 2n}\\ \\ \sf{\implies \frac{18}{2} = n}\\ \\ \sf{\implies \color{purple}n= 9}[/tex]

   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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   Reply

2. 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°

   [tex]=2n – 4 = \frac{1260°}{90°} = 14[/tex]

   2n = 18

   n = 9

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

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