Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises: 10

Answer

$\angle$1=39$^{\circ}$ $\angle$4=39$^{\circ}$ $\angle$2=51$^{\circ}$ $\angle$3=51$^{\circ}$ $\angle$5=39$^{\circ}$ $\angle$6=39$^{\circ}$

Work Step by Step

Given: $\overline{UZ}$$\parallel$$\overline{XZ}$ $\overline{VY}$$\bot$$\overline{UW}$ $\overline{VY}$$\bot$$\overline{XZ}$ lets find the value of x according to the figure and question its is clear that $\angle$1=$\angle$4 and $\angle$2=$\angle$3 and $\angle$1+$\angle$4+$\angle$2+$\angle$3= 180$^{\circ}$ so, 4x+3+4x+3+6x-3+6x-3=180 20x=180 x=9 therefore, $\angle$1=$\angle$4=4(9)+3=39$^{\circ}$ $\angle$2=$\angle$3=6(9)-3=51$^{\circ}$ and $\angle$5=39$^{\circ}$ and $\angle$6=39$^{\circ}$ because both are alternate angles of $\angle$1 and $\angle$4 respectively.
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