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 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 285: 12d

Answer

$m\angle DGE=38^{\circ}$

Work Step by Step

If two inscribed angles intercept the same arc, then the two angles are congruent. Since $\angle F$ intercepts the same arc as $\angle DGE$, these two angles are congruent. $m\angle F=m\angle DGE=38^{\circ}$
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