Question

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

Answer 1

$\huge\bold\color{red} {{\boxed{\boxed{ \mathtt{{☆Answer☆}}}}}}$

Number of sides :- 8 Sides.

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Solution

• 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

$\mathtt{⇒(n−2)×180=135n}$

$\mathtt{⇒180(n−2)=135n}$

$\mathtt{⇒180n−360=135n}$

$\mathtt{⇒180n−135n=360}$

$\mathtt{⇒45n=360}$

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

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