The difference between an exterior angle of (n – 1) sided regular polygon and an exterior angle of (
The difference between an exterior angle of (n – 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6°, then the value of ‘n’ is
Explanation
The exterior angle of a regular polygon equals 360 degrees divided by the number of sides. For an n minus 1 sided polygon, the exterior angle is 360 over parenthesis n minus 1. For an n plus 2 sided polygon, it is 360 over parenthesis n plus 2.
Set up the equation for the difference: 360 divided by parenthesis n minus 1 minus 360 divided by parenthesis n plus 2 equals 6. Find a common denominator of parenthesis n minus 1 times parenthesis n plus 2. This gives 360 times parenthesis n plus 2 minus 360 times parenthesis n minus 1 all divided by common denominator equals 6.
Simplify the numerator: 360n plus 720 minus 360n plus 360 equals 1080. So 1080 divided by parenthesis n minus 1 times parenthesis n plus 2 equals 6. Cross multiply: 1080 equals 6 times parenthesis n² plus n minus 2. Solve: 180 equals n² plus n minus 2, so n² plus n minus 182 equals 0. Factor to get n equals 13 or n equals negative 14. Since sides must be positive, n equals 13.