Math, asked by safeshopkunalp, 2 days ago

15. What is the number of sides of a regular polygon whose interior angle is of 135° each​


Answered by Anonymous

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Number of sides :- 8 Sides.



  • Let the number of sides and angles of the polygon be 'n'.

  • The formula for the sum S of the n interior angles of an n- sided polygon is S=(n−2)×180°

  • Since the polygon is regular, all its n interior angles are the same.

Therefore the sum of them is n×135° =135n°

So, we also have S =135n°

So, setting angels equal as shown below:

(n−2)×180° =135n






 \color{green}\ { \boxed{ \mathtt{{⇒n=8}}}}

So, the regular polygon has 8 sides and is therefore, an octagon.

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