Question

If m arc CD = 143°, and m arc AB = 39°, what is m∠ DEC ?

Answer 1

`m\angle DEC=91^o`

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

`m\angle DEC=(1)/(2)[arc\ AB+arc\ DC]`

substitute the given values

`m\angle DEC=(1)/(2)[39^o+143^o]`

`m\angle DEC=(1)/(2)[182^o]`

`m\angle DEC=91^o`