   Chapter 6.1, Problem 29E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# An amusement park ride (the “Octopus”) has eight support arms that are equally spaced about a circle. What is the measure of the central angle formed by two consecutive arms?

To determine

To calculate:

The measure of the central angle formed by two consecutive arms if there are 8 support arms.

Explanation

Given:

An amusement park ride (the “Octopus”) has eight support arms that are equally spaced about a circle.

Postulate used:

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, congruent arcs are arcs with equal measures.

Since, the sum of the measures of the consecutive arc that form a circle is 360o.

Calculation:

Consider, the figure given below:

Since, in a circle, congruent arcs are arcs with equal measures.

mAB=mBC

mBC=mCD

mCD=mDE

mDE=mEF

Similarly

mEF=mFG

mFG=mGA

Since, the sum of the measures of the consecutive arc that form a circle is 360o.

mAB+mBC+mCD+mDE+mEF+mFG+mGA=360o

By using the above result we obtain

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