We are given an inscribed regular heptagon.

Before we begin, let's review some key definitions about the parts of inscribed polygons.

Center: The center of an inscribed regular polygon is the center of the circle.
Radius: The radius of an inscribed regular polygon is the radius of the circle.
Apothem: An apothem is a segment from the center of the regular polygon perpendicular to a side.
Central Angle: A central angle of a regular polygon has its vertex at the center of the polygon and its sides pass through consecutive vertices of the polygon.

Now let's identify these features in the given inscribed polygon.

Finally, we want to find the measure of the central angles for this inscribed polygon. The measure of each central angle of a regular

n -

gon is

\frac{3 6 0}{n} .

Since we are given a regular heptagon, we have that

n = 7 .

Let's substitute this value in the formula and simplify.

\frac{3 6 0}{n}

$n = 7$

\frac{3 6 0}{7}

Calculate quotient

51.428571 \dots

Round to $1$ decimal place(s)

51.4

The measure of a central angle is about

51 . 4^{\circ} .

Exercise