Answer:
[tex]m<FEH=86\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
step 1
Find the measure of arc EF
[tex]m<FHE=\frac{1}{2}(arc\ EF)[/tex]
we have
[tex]m<FHE=45\°[/tex]
substitute
[tex]45\°=\frac{1}{2}(arc\ EF)[/tex]
[tex]arc\ EF=90\°[/tex]
step 2
Find the measure of arc EH
[tex]m<EGH=\frac{1}{2}(arc\ EH)[/tex]
we have
[tex]m<EGH=49\°[/tex]
substitute
[tex]49\°=\frac{1}{2}(arc\ EH)[/tex]
[tex]arc\ EH=98\°[/tex]
step 3
Find the measure of arc FGH
[tex]arc\ FGH=360\°-(arc\ EH+arc\ EF)[/tex]
substitute the values
[tex]arc\ FGH=360\°-(98\°+90\°)[/tex]
[tex]arc\ FGH=172\°[/tex]
step 4
Find the measure of angle FEH
[tex]m<FEH=\frac{1}{2}(arc\ FGH)[/tex]
we have
[tex]arc\ FGH=172\°[/tex]
substitute
[tex]m<FEH=\frac{1}{2}(172\°)=86\°[/tex]
