Given: circle k(O), ED diameter, m∠OEF=32°, mEF =(2x+10)° Find: x
Accepted Solution
A:
Answer:[tex]x=53[/tex]Step-by-step explanation:step 1Find the measure of arc DFwe know thatThe inscribed angle measures half that of the arc comprisingso[tex]m<OEF=\frac{1}{2}(arc\ DF)[/tex]we have[tex]m<OEF=32\°[/tex]substitute[tex]32\°=\frac{1}{2}(arc\ DF)[/tex][tex]arc\ DF=64\°[/tex]step 2Find the measure of xwe know that[tex]arc\ DF+arc\ EF=180\°[/tex] ---> is half the circlewe have[tex]arc\ DF=64\°[/tex][tex]arc\ EF=(2x+10)\°[/tex]substitute[tex]64\°+(2x+10)\°=180\°[/tex][tex]2x\°=180\°-74\°[/tex][tex]2x\°=106\°[/tex][tex]x=53[/tex]