Answer:
[tex]arc\ RF=80^o[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
step 1
Find the measure of the arc PQR
[tex]109^o=\frac{1}{2}[arc\ PQR][/tex]
[tex]arc\ PQR=218^o[/tex]
step 2
Find the measure of arc QR
[tex]arc\ PQR=arc\ PQ+arc\ QR[/tex]
we have
[tex]arc\ PQR=218^o[/tex]
[tex]arc\ PQ=74^o[/tex]
substitute
[tex]218^o=74^o+arc\ QR[/tex]
[tex]arc\ QR=144^o[/tex]
step 3
Find the measure of the arc QRF
[tex]112^o=\frac{1}{2}[arc\ QRF][/tex]
[tex]arc\ QRF=224^o[/tex]
step 4
Find the measure of arc RF
[tex]arc\ QRF=arc\ QR+arc\ RF[/tex]
we have
[tex]arc\ QRF=224^o[/tex]
[tex]arc\ QR=144^o[/tex]
substitute
[tex]224^o=144^o+arc\ RF[/tex]
[tex]arc\ RF=80^o[/tex]
