Question

Find the value of n for the regular n-gon described.
Each interior angle of the regular n-gon has a measure of 75.2º.

Answer 1

Answer:

n = 3.44

Step-by-step explanation:

The interior angle of a regular n-gon is given by the formula;

$I = \frac {180(n-2)}{n}$

Where,

• I represents the interior angle.

• n represents the number of sides.

Given that interior angle = 75.2°

Substituting into the equation, we have;

$75.2 = \frac {180(n-2)}{n}$

Cross multiplying, we have;

$75.2n = 180(n-2)$

$75.2n = 180n - 360$

Rearranging the equation, we have;

$180n - 75.2n = 360$

$104.8n = 360$

$n = \frac {360}{104.8}$

n = 3.44

Therefore, the number of sides "n" of the regular n-gon described is 3.44.