Chapter 11.5, Problem 34SPR

To determine

To Find: The measure of the central angle.

Answer to Problem 34SPR

The value of the central angle is $90°$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

From, the given figure the centre of the square is $R$ , the radius of the square is

  $\overline{RX}$ and the apothem is $\overline{RS}$ .

Consider the central angle of the regular polygon has the vertex at the centre of the polygon and its sides pass through consecutive vertices of the polygon.

Then, the central angle of square is,

  $\angle YRX$

The measure of the each central angle of regular n-gon is,

  $\frac{360}{n}$

Since, as the square of the four sides. Then, the 4-gon measure of each central of the square is,

  $\begin{array}{c}\frac{360}{n}=\frac{360}{4}\\ =90°\end{array}$