Chapter 6.1, Problem 29E

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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

**Calculation:**

Consider, the figure given below:

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

Similarly

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

By using the above result we obtain

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