Question

how many sides does a regular polygon have if each of its interior angles measure 180°?​

Answer 1

Answer:

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24 sides

The sum of the interior angles in any polygon is 180(n - 2) degrees. Then, since each angle in a regular polygon is the same, each interior angle has a measure of 180(n - 2)/n degrees. ==> n = 24. Thus, the polygon has 24 sides.

Answer 2

No such polygon consists of 180° as its interior angles.

Given:

The interior angle of a polygon is 180°  

To find:

How many sides does a regular polygon have

Solution:

Condition used:

Sum of interior angles = (n-2) × 180°    

Where 'n' is the number of sides of the polygon

Let 'n' be the number of sides of the polygon which have 180° as each interior angles

Sum of the interior angles = n × 180°  

Using the above formula,

Sum of interior angles = (n-2) × 180°    

=> n × 180° = (n-2) × 180°    

=> n = n - 2

=> n - n = 2

=> 0 = 2  

Here, we can't solve for 'n'

So, the polygon cannot be exist

Therefore,

No such polygon consists of 180° as its interior angles.

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