   Chapter 7.3, Problem 34E 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

Given: Regular pentagon JKLMN (not shown) with diagonals L N ¯   and   K N ¯ .Find: m ∠ L N K

To determine

To find:

The measure of mLNK.

Explanation

Approach:

The measure of interior angle of regular polygon of n sides is given by (n2)180n

Calculation:

Consider the figure.

Interior angles of regular pentagon =(52)1805=108

Therefore, LMN=MNJ=NJK=108

Since, JKLMN is a regular pentagon.

Therefore, JK=KL=LM=MN=NJ

In triangle KJN, JK=NJ

The angles opposite to equal sides are always equal.

Therefore, b = d

Use the angle sum property of triangle,

b+c+d=180d+108+d=1802d=1801082d=72d=36

In triangle KMN, ML=MN

The angles opposite to equal sides are always equal

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