Chapter 11.4, Problem 8PPS

To determine

To find: The centre, radius, an apothem and a central angle of the given polygon. Then, find the measure of the central angle.

Answer to Problem 8PPS

The centre is at $X$ , the radius is $\overline{XV}$ , the apothem is $\overline{XY}$ and the central angle $\angle VXT$ is $72°$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the centre of the regular polygon is the centre of the polygon’s circumscribed circle then, the centre is at X.

Consider the radius of the polygon is the radius of the circle that is line XV.

Consider the apothem is the segment drawn from the centre of the regular polygon perpendicular to the side of the polygon that is line XY.

Consider that the central angle of the regular polygon has the vertex at the centre of the polygon and it passes through consecutive vertices of the polygon.

Thus, the central angle of the regular polygon is $\angle VXT$ . Thus, the central angle measure is,

  $\begin{array}{c}\frac{360}{n}=\frac{360}{5}\\ =72\end{array}$

Thus, the centre is at $X$ , the radius is $\overline{XV}$ , the apothem is $\overline{XY}$ and the central angle $\angle VXT$ is $72°$ .