   Chapter 1.4, Problem 30E ### 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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# On the protractor shown, N P ⇀ bisects ∠ M N Q . Find x . Exercises 3 0 , 3 1

To determine

To find:

The measure of x.

Explanation

The ray that separates a angle into congruent angles is known as Bisector.

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

Given:

The given figure is,

The ray NP bisects MNQ.

Calculation:

Consider the figure (1) with points R and S.

Figure (1)

From figure (1) it can be seen that the measure of SNQ is 53°.

The measure of MNS can be written as,

mMNS=mMNP+mMNQ+mSNQx=mMNP+mMNQ+mSNQ(1)

NP is the bisector of MNQ.

mMNP=mPNQ

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