Question

Is it possible to have a regular polygon with an exterior angle of measure 25° ?​

Answer 1

Answer:

Not Possible

Step-by-step explanation:

Given :-

An exterior angle = 25°

To find :-

It is possible to have a regular polygon with an exterior angle of measure 25° ?

Solution :-

Given exterior angle = 25°

We know that

Each exterior angle of a regular polygon of n sides is 360°/n

=> 360°/n = 25°

=> 360° = 25°×n

=> n×25° = 360°

=> n = 360°/25°

=> n = 72/5

Therefore, n = 72/5

Number of sides can't be a fraction.

It must be a natural number.

So, There is no regular polygon having the exterior angle of 25° .

Answer:-

It is not possible to have a regular polygon with an exterior angle of measure 25° .

Used formulae:-

Each exterior angle of a regular polygon of n sides is 360°/n

Points to know:-

→ A polygon of all sides and all angles are equal is called a regular polygon.

→ Each exterior angle of a regular polygon of n sides is 360°/n

→ Sum of all exterior angles of a regular polygon is 360°

→ Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°

→ Sum of all interior angles of a regular polygon is (n-2)×180°

Answer 2

Given:-

• $\tt \: Exterior \: Angle \: = \: 25°$

To Do:-

• $\tt \: Is \: it \: possible \: to \: have \: a \: \\ \tt regular \: polygon \: with \: an \: \\ \tt exterior \: angle \: of \: measure \: 25°?$

Let's Start:-

• $\tt \: It \: is \: not \: possible \: to \: have \: a \: \\ \tt \: regular \: polygon  \: \tt \: each \: of \: \\ \tt \: whose \: exterior \: angle \: is \: 25.$

Reason:-

• $\tt \: The \: formula \: is \: (360/n).. \: and \: \\ \tt \: 360 \: is \: not \: exactly \: divisible \\ \tt by \: 25.$