Can you give me a regular polygon with side lengths equal to 3cm each angle measurement's are 180 degree 

A regular polygon is a polygon with all sides and angles equal. The sum of the interior angles of a polygon with \( n \) sides (an \( n \)-gon) is given by the formula:

\[ \text{Sum of interior angles} = (n-2) \times 180^\circ \]

Each interior angle of a regular \( n \)-gon is:

\[ \text{Each interior angle} = \frac{(n-2) \times 180^\circ}{n} \]

You mentioned that each angle is 180 degrees. Let's substitute this into the formula and solve for \( n \):

\[ 180^\circ = \frac{(n-2) \times 180^\circ}{n} \]

Dividing both sides by 180 degrees:

\[ 1 = \frac{n-2}{n} \]

To solve for \( n \), we multiply both sides by \( n \):

\[ n = n - 2 \]

\[ 0 = -2 \]

This is a contradiction, meaning there is no regular polygon with each interior angle equal to 180 degrees. 

A polygon with angles of 180 degrees doesn't exist because angles of 180 degrees imply a straight line

Explore the concept of regular polygons with equal side lengths and each angle measuring 180 degrees. Learn about the formulas for the sum of interior angles and each interior angle of a polygon. Suitable for students in Grades 9-12.

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