Chapter 13.3, Problem 47SPR

To determine

To calculate:

The measure of small arc.

Answer to Problem 47SPR

The measure of small arc is $45°$ .

Explanation of Solution

Given information:

  

Calculation:

A stained glass that contains the points A, B, C, D, E, F, G, and H has the following design.

  

Since there are $8$ small arcs around the circle, which are given by:

  $\measuredangle AB,\measuredangle BC,\measuredangle CD,\measuredangle DE,\measuredangle EF,\measuredangle FG,\measuredangle GH,\measuredangle HA$ , and these 8 arcs are congruent, the measure of each arc is found by dividing $360°$ degrees by $8$ .

Let,

Measure of small arc = $MS$

Thus, the measure of small arc can be calculated as:

  $\begin{array}{l}MS=\frac{360°}{8}\\ MS=45°\end{array}$

Hence, the measure of small arc is $45°$ .