Question

Find the measure of the arc or angle indicated.

Answer 1

Answer:

$arc\ RF=80^o$

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

$109^o=\frac{1}{2}[arc\ PQR]$

$arc\ PQR=218^o$

step 2

Find the measure of arc QR

$arc\ PQR=arc\ PQ+arc\ QR$

we have

$arc\ PQR=218^o$

$arc\ PQ=74^o$

substitute

$218^o=74^o+arc\ QR$

$arc\ QR=144^o$

step 3

Find the measure of the arc QRF

$112^o=\frac{1}{2}[arc\ QRF]$

$arc\ QRF=224^o$

step 4

Find the measure of arc RF

$arc\ QRF=arc\ QR+arc\ RF$

we have

$arc\ QRF=224^o$

$arc\ QR=144^o$

substitute

$224^o=144^o+arc\ RF$

$arc\ RF=80^o$