To find the number of sides nnn of a regular polygon given that each interior angle is 1°, we use the formula for the interior angle of a regular polygon:
Interior angle=180(n−2)n\text{Interior angle}=\frac{180(n-2)}{n}Interior angle=n180(n−2)
Here, the interior angle is given as 1°. So,
1=180(n−2)n1=\frac{180(n-2)}{n}1=n180(n−2)
Solving for nnn involves these steps:
1×n=180(n−2)1\times n=180(n-2)1×n=180(n−2)
n=180n−360n=180n-360n=180n−360
n−180n=−360n-180n=-360n−180n=−360
−179n=−360-179n=-360−179n=−360
n=360179≈2.01n=\frac{360}{179}\approx 2.01n=179360≈2.01
Since nnn must be an integer greater than or equal to 3 for a polygon, a regular polygon cannot have an interior angle of 1°. This means no regular polygon exists with each interior angle equal to 1° because the number of sides calculated is not a valid polygon number.
