Question

If each interior angle of a regular polygon is 144°, then what will be the number of sides? ANSWER WITH PROPER JUSTIFICATION

Answer 1

Given,

Each int. angle = 144°

Since,

Each int. ∠ = {(2n-4)×90°}/n,  where n is the number of sides

⇒ 144° = {(2n-4)×90°}/n

⇒144°×n =  (2n-4)×90°

⇒144n° = 180n° - 360°

⇒180n°-144n° = 360°

⇒36n° =360°

⇒n = 360°/36° = 10

So, the number of sides is 10.

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