## Elementary Geometry for College Students (7th Edition)

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