Question

Find the number of sides of a regular Polygon if the Sum of its interior angle is 540

Step by step
plz ​

Answer 1

Answer

5

Step-by-step explanation:

Sum of interior angles =540

therefore

180(n-2) = 540

n-2 = 540 ÷ 180

n-2 = 3

n= 3+2

n =5

therefore

no of sides = 5

Answer 2

Answer:

5 sides

Step-by-step explanation:

Let there are n sides in the polygon that has a sum of internal angles 540

then,

(n−2)×180° =540°

n−2=3

n=5

It have 5 sides so it is a pentagon.

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The sum of the interior angles of a polygon is equal to 2 less than the number of sides the polygon has multiplied by 180.

This can be expressed in an equation as:

a=180(s-2) where a equals the sum of interior angles and s equals the number of sides the polygon has.

If we plug 540 in as the 'a' value, we find that:

540=180(s-2)

We can then divide both sides of the equation by 180:

3=s-2

Finally, we can add 2 to both sides of the problem:

5=s

Therefore we find that the polygon has 5 sides.