Elementary Geometry for College Students (7th Edition) Clone

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

Chapter 4 - Review Exercises - Page 217: 19

Answer

$m\angle E=108^{\circ}$, $m\angle F= m\angle G=72^{\circ}$

Work Step by Step

1. Given isosceles trapezoid $DEFG$ with $DE \parallel GF$, the pairs of congruent base angles will be $m\angle E=m\angle D$ and $m\angle F= m\angle G$. If $m\angle D=108^{\circ}$, then $m\angle E=108^{\circ}$. 2. The four interior angles of a quadrilateral sum to $360^{\circ}$. $360-108-108=144$ 3. Since $m\angle F= m\angle G$, the remaining 144 degrees needs to be divided equally between the two angles. $144\div2=72$ $m\angle F= m\angle G=72^{\circ}$
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