Question

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

Answer 1

Answer:

$m\angle DEC=91^o$

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

$m\angle DEC=\frac{1}{2}[arc\ AB+arc\ DC]$

substitute the given values

$m\angle DEC=\frac{1}{2}[39^o+143^o]$

$m\angle DEC=\frac{1}{2}[182^o]$

$m\angle DEC=91^o$