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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Chapter 1.4, Problem 31E, Exercises 30,31 On the protractor shown for Exercise 30, MNP and PNQ are complementary. Find x.

Exercises 3 0 , 3 1

On the protractor shown for Exercise 30, M N P and P N Q are complementary. Find x .

To determine

To find:

The measure of x.

Explanation

Given:

The given figure is,

MNP and PNQ are complementary.

Definition:

If the sum of two angles is 90° then the angles are known as complementary angles. Each angle in the pair is the complement of the other angle.

Angle addition postulate says that,

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

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)

MNP and PNQ are complementary.

mMNP+mPNQ=90°mMNP=90°mPNQ

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