Question

for the regular n-gon shown to the right, give the measures of the interior, exterior, and central angles.
the measure of each interior angle is $square^circ$, the measure of each exterior angle is $square^circ$, and the measure of each central angle is $square^circ$.
(type an integer or a simplified fraction)

Explanation:

Step1: Identify n (number of sides)

The figure is a regular 7-gon, so $n=7$.

Step2: Calculate interior angle

Use interior angle formula: $\frac{(n-2)\times180^\circ}{n}$
$\frac{(7-2)\times180^\circ}{7}=\frac{5\times180^\circ}{7}=\frac{900}{7}^\circ$

Step3: Calculate exterior angle

Use exterior angle formula: $\frac{360^\circ}{n}$
$\frac{360^\circ}{7}$

Step4: Calculate central angle

Use central angle formula: $\frac{360^\circ}{n}$
$\frac{360^\circ}{7}$

Answer:

The measure of each interior angle is $\frac{900}{7}^\circ$, the measure of each exterior angle is $\frac{360}{7}^\circ$, and the measure of each central angle is $\frac{360}{7}^\circ$