Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 275: 8

Answer

$m\angle DOE=48^{\circ}$

Work Step by Step

The measure of an entire circle equals $360^{\circ}$. Subtract out the major arc $ECABD$, or $312^{\circ}$. $360-312=48$ Minor arc $DE=48^{\circ}$. The measure of a central angle is equal to its intercepted arc. Thus, $m\angle DOE=48^{\circ}$.

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