Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 2 - Section 2.4 - The Angles of a Triangle - Exercises - Page 106: 16


x=108$^{\circ}$ y=44$^{\circ}$ z=47$^{\circ}$

Work Step by Step

The sum of the measures of the angles within a triangle is 180$^{\circ}$. m$\angle$NMR+m$\angle$MNR+m$\angle$MRN=180 43+65+m$\angle$MRN=180 m$\angle$MRN=72$^{\circ}$ Angle MRN and x are supplementary. m$\angle$MRN+x=180 72+x=180 x=108$^{\circ}$ x+y+m$\angle$P=180 108+y+28=180 y=44$^{\circ}$ Angle NRQ and x are vertical angles so they are congruent. Angle RNQ is complimentary to angle MNR. m$\angle$MNR+m$\angle$RNQ=90 65+m$\angle$RNQ=90 m$\angle$RNQ=25$^{\circ}$ m$\angle$RNQ+m$\angle$NRQ+z=180 25+108+z=180 z=47$^{\circ}$
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