   Chapter 1.4, Problem 43E ### 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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# Exercises 44, 45If m ∠ T S U = x + 2 z , m ∠ U S V = x − z , and m ∠ V S W = 2 x − z , find x if m ∠ T S W = 60 . Also, find z if m ∠ U S W = 3 x − 6 .

To determine

To find:

The value of x and z.

Explanation

Given:

mTSU=x+2z, mUSV=xz, mVSW=2xz, mTSW=60 and mUSW=3x6.

The given figure is,

Definition:

If a point say M lies in the interior of PQR, then mPQM+mRQM=mPQR.

Approach:

The given figure is,

Figure (1)

Consider the figure (1),

U and V are the interior point of the angle TSW.

mTSU is x+2z, mUSV is xz, mVSW is 2xz and mTSW is 60°.

Use above mentioned angle addition postulate to solve for x.

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