Question

the sum of interior angle of a polygonis 1440°.how many sides does this polygon have

Answer 1

You haven't indicated whether or not this is a REGULAR polygon (one whose sides are all of equal length) but I'll assume that it is.

You can start with the formula for the sum of the interior angles (S) of a regular polygon of n-sides: s=(N-2)/180

Since you know that this sum is 1440 degrees, you can substitute this into the formula and solve for n, the number of sides.

1440=(N-2)/180 Divide both sides by 180

8=n-2 Add 2 to both sides.

n=10

The regular polygon has 10 sides. This is known as a decagon.

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Answer 2

Number of sides of the polygon = 10

Given :

The sum of interior angle of a polygon is 1440°

To find :

Number of sides of the polygon

Formula :

The sum of interior angles of a polygon with n sides = (n - 2) × 180°

Solution :

Step 1 of 2 :

Write down sum of interior angles of a polygon

The sum of interior angles of the polygon = 1440°

Step 2 of 2 :

Measure number of sides of the polygon

Let number of sides = n

The sum of interior angles of the polygon = 1440°

By the given condition ,

(n - 2) × 180° = 1440°

⇒ n - 2 = 1440°/180°

⇒ n - 2 = 8

⇒ n = 8 + 2

⇒ n = 10

Hence number of sides of the polygon = 10

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