   Chapter 7.3, Problem 33E 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 RSTVQ with equilateral Δ PQRFind: m ∠ V P S To determine

To find:

The measure of VPS.

Explanation

Given,

The regular pentagon QRSTV

and mPQR is equilateral.

Calculation:

It is given that ΔPQR is an equilateral triangle.

Therefore, mPQR=60

Interior angle of regular polygon is 108°.

mVQR=mVTS=108mVQP=mVQRmPQR=10860=48

Triangle QVP is isosceles as QP=QV.

Let QVP=QPV=x

In triangle QVP

PQV+2x=180

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