Answer:
n = 3.44
Step-by-step explanation:
The interior angle of a regular n-gon is given by the formula;
[tex] I = \frac {180(n-2)}{n} [/tex]
Where,
- I represents the interior angle.
- n represents the number of sides.
Given that interior angle = 75.2°
Substituting into the equation, we have;
[tex] 75.2 = \frac {180(n-2)}{n} [/tex]
Cross multiplying, we have;
[tex] 75.2n = 180(n-2)[/tex]
[tex] 75.2n = 180n - 360[/tex]
Rearranging the equation, we have;
[tex] 180n - 75.2n = 360[/tex]
[tex] 104.8n = 360[/tex]
[tex] n = \frac {360}{104.8}[/tex]
n = 3.44
Therefore, the number of sides "n" of the regular n-gon described is 3.44.
