Answer:
[tex]m\angle DEC=91^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
so
[tex]m\angle DEC=\frac{1}{2}[arc\ AB+arc\ DC][/tex]
substitute the given values
[tex]m\angle DEC=\frac{1}{2}[39^o+143^o][/tex]
[tex]m\angle DEC=\frac{1}{2}[182^o][/tex]
[tex]m\angle DEC=91^o[/tex]
