Answer:
The value of x is [tex]53\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc DF
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<OEF=\frac{1}{2}(arc\ DF)[/tex]
we have
[tex]m<OEF=32\°[/tex]
substitute
[tex]32\°=\frac{1}{2}(arc\ DF)\\ arc\ DF=64\°[/tex]
step 2
Find the measure of x
we know that
[tex]arc\ DF+arc\ EF=180\°[/tex] ---> is a semi circle
we have
[tex]arc\ DF=64\°\\ arc\ EF=(2x+10)\°[/tex]
substitute
[tex]64\°+(2x+10)\°=180\°\\ 2x\°=180\°-74\°\\ 2x\°=106\°\\ x=53\°[/tex]
