Question

Class 8 maths chapter 3 exercise 3.2 question 4 how many sides does a regular polygon have if each of its interior angle is 165

Answer 1

Answer:

24

Step-by-step explanation:

angle=(n-2)×180/n

=>165=(n-2)×180/2

=>165n=180n-360

=>180n-165n=360

=>15n=360

=>n=360/15=24

Answer 2

Answer :

• The regular polygon with interior angles each measures 165⁰ is 24 sides

Given :

• Interior angle is 165

To find :

• How many sides does a regular polygon have ?

Solution :

• Let the number of sides of regular polygon be n

As we know that, interior angle of a regular polygon formula,

• 180⁰(n - 2)/n

Where, n is sides

Given interior angle is 165⁰ so,

》180⁰n(n - 2) = 165⁰

》180⁰ (n - 2) = 165⁰n

Now , Adding 360⁰ on both sides we get,

》180⁰n - 360⁰ + 360⁰ = 165⁰ + 360⁰

》180⁰n = 165⁰n + 360⁰

Now Subtracting both sides by 165⁰ on this both sides we get

》180⁰n - 165⁰n = 165⁰n + 360⁰n - 165⁰n

》15⁰n = 360⁰

》n = 360⁰/15⁰

》n = 24

Hence, The regular polygon with interior angles each measures 165⁰ is 24 sides