Question

it is a possible to have a regular polygon whose exterior angle is 182 degree give reason​

Answer 1

Given:

Measure of an exterior angle of a polygon = 182°

To Find:

Possibility of a regular polygon having an exterior angle = 182°

Solution:

Since, measure of an exterior angle of a regular polygon is given by the formula,

Exterior angle = $\frac{360}{\text{Number of sides in the polygon}}$ = $\frac{360}{\text{n}}$

If the measure of the exterior angle = 182°

182 = $\frac{360}{n}$

n = $\frac{360}{182}$

n = 1.98 ≈ 2

For n = 2 is not possible existence of a polygon is not possible because minimum number of the sides in a polygon should be 3.

Or triangle is a polygon having the least number of sides = 3.

Answer 2

Answer:

Not possible

Step-by-step explanation:

Measure of each interior angle = 180° - 182° = - 2°

Sum of angles in any polygon is given by (n - 2) x 180°, where n is the number of sides.

 Let this polygon be of 'n' sides. A polygon contains same of lines as that of angles, so if number of sides is 'n', so the number of angles is also 'n' .   Hence,

⇒ sum of all angles = (n - 2) x 180°

⇒ (-2)° + (-2)° + (-2)° + ... upto n times = (n - 2) x 180°

⇒ n(-2°) = n(180°) - 2(180°)

⇒ 2(180°) = n(180°) - n(-2°)

⇒ 360° = n(180° + 2°) = n(182°)

⇒ 360° = n(182°)

⇒ (360°/182°) = n

⇒ 1.9 = n = number of sides,    which is not a counting number, hence it is not possible for a regular polygon to have exterior angle 182°.