70 POINTS!!!!!!!!!! Given: E, F, Q, D∈k(O),O ∈ ED, m∠DFQ = 10°, measure of arc EF = 28° Find: Angles of △EFQ

Answer:The measures of angles of triangle EFQ are1) [tex]m\angle EFQ=100\°[/tex]2) [tex]m\angle FEQ=66\°[/tex]3) [tex]m\angle EQF=14\°[/tex]Step-by-step explanation:step 1Find the measure of arc QDwe know thatThe inscribed angle is half that of the arc it comprises.[tex]m\angle DFQ=\frac{1}{2}(arc\ QD)[/tex]substitute the given value[tex]10\°=\frac{1}{2}(arc\ QD)[/tex][tex]20\°=(arc\ QD)[/tex][tex]arc\ QD=20\°[/tex]step 2Find the measure of arc FQwe know that[tex]arc\ QD+arc\ FQ+arc\ EF=180\°[/tex] ---> because ED is a diameter (the diameter divide the circle into two equal parts)substitute the given values[tex]20\°+arc\ FQ+28\°=180\°[/tex][tex]arc\ FQ=180\°-48\°=132\°[/tex]step 3Find the measure of angle EFQwe know thatThe inscribed angle is half that of the arc it comprises.[tex]m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)[/tex]substitute the given value[tex]m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°[/tex]step 4Find the measure of angle FEQwe know thatThe inscribed angle is half that of the arc it comprises.[tex]m\angle FEQ=\frac{1}{2}(arc\ FQ)[/tex]substitute the given value[tex]m\angle FEQ=\frac{1}{2}(132\°)=66\°[/tex]step 5Find the measure of angle EQFwe know thatThe inscribed angle is half that of the arc it comprises.[tex]m\angle EQF=\frac{1}{2}(arc\ EF)[/tex]substitute the given value[tex]m\angle EQF=\frac{1}{2}(28\°)=14\°[/tex]