   Chapter 6.1, Problem 26E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Five points are equally spaced on a circle. A five-pointed star (pentagram) is formed by joining nonconsecutive points two at a time. What is the degree measure of an arc determined by two consecutive points?

To determine

To calculate:

The degree measure of an arc determined by two consecutive points.

Explanation

Given:

Five points are equally spaced on a circle. A five-pointed star (pentagram) is formed by joining nonconsecutive points two at a time.

Central angle postulate:

In a circle, the degree measure of a central angle is equal to the degree measure of its intercepted arc.

Congruent arcs:

In a circle or congruent circles, congruent arcs are arcs with equal measures.

Theorem:

In a circle or congruent circles, congruent minor arcs have congruent central angles.

Calculation:

Consider five points that are equally spaced on a circle. Construct a star by connecting those points as shown below.

Thus the arcs formed are congruent arcs.

Hence if we consider the central angles for each arc, they will be congruent because the arcs are congruent...

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