Question

is it possible to have a regular polygon with each exterior angle of 138 degree​

Answer 1

Answer:

No, it's not possible.

Explanation:

To check whether it's possible or not, we have to find the number of sides of the polygon having each exterior angles of 138°.

Sum of all exterior angles of a polygon is 360°

Number of sides :

➡ Sum of all exterior angles/Measure of each exterior angle

➡ 360°/ 138°

➡ 2.6

The number of sides is 2.6, Such polygon doesn't exist. So, it's not possible.

Related question:

Is it possible to have a regular polygon having each of the exterior angle is 50 ?degree

https://brainly.in/question/29466780

Answer 2

Answer

No, it's not possible  to have a regular polygon with each exterior angle of 138 degree​.

$\huge \bf \color{fuchsia} {Verification\checkmark}$

To check whether it's [ regular polygon with each exterior angle of 138 degree​] possible or not, we have to find the number of sides of the polygon having each exterior angles of 138°.

Sum of all exterior angles of a polygon is 360°

Number of sides :

$\color{blue} {\looparrowright}$ Sum of all exterior angles / Measurement of each exterior angle

$\color{blue} {\looparrowright}$ 360°/ 138°

$\color{blue} {\looparrowright}$ 2.6

$\color{blue} {\looparrowright}$The number of sides is 2.6, Such polygon doesn't exist. So, it's not possible to have a regular polygon with each exterior angle of 138 degree​.

or ,

$\color{blue} {\looparrowright}$No. of sides = n

$\color{blue} {\looparrowright}$Each interior angle = 155°

$\color{blue} {\looparrowright}$∴ ((2n – 4) × 90°)/n = 155°

$\color{blue} {\looparrowright}$180n - 360° = 155n

$\color{blue} {\looparrowright}$180n – 155n = 360°

$\color{blue} {\looparrowright}$25n = 360°

$\color{blue} {\looparrowright}$n = 360°/25°

$\color{blue} {\looparrowright}$n = 72°/5

$\color{blue} {\looparrowright}$Which is not a whole number.

$\color{blue} {\looparrowright}$hence , its not possible.

Step-by-step explanation:

i hope it helps