Question

Is it possible to have a regular polygon whose interior angle 145

Answer 1

the answer of this question is no

Answer 2

$\small \mathcal \colorbox{lightblue}{solution}$

Let the number of sides of the given polygon be n .

As per the question , (n-2) × 180⁰ = 145⁰n

➜ 180⁰-360⁰ = 145⁰n

➜ (180⁰n-360⁰)= 360⁰

➜ 35n= 360⁰

$n = \frac{360^{o} }{35 ^{o}} \: = \frac{72}{7}$

$= 10\frac{2}{7}$

It is not a while number .

Therefore, it is not possible to have a regular polygon whose each interior angle is 145 ⁰.