   Chapter 6.1, Problem 27E 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

A ceiling fan has equally spaced blades. What is the measure of the angle formed by two consecutive blades if there are a) 5 blades? b) 6 blades? To determine

(a)

To Find: The measure of the angle formed by two consecutive blades if there are 5 blades.

Explanation

Given:

A ceiling are equally spaced 5 blades.

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, the 5 blades are equally spaced.

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

mAB=mBC

mBC=mCD

mCD=mDE

And

mDE=mEA

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

mAB+mBC+mCD+mDE+mEA=360o

By using the above result we obtain

To determine

(b)

To calculate:

The measure of the angle formed by two consecutive blades if there are 6 blades.

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