Find the measure of the arc or angle indicated.

Question

asked Oct 12, 2021 144k views

1 Answer

Pourjour · Answer 1 · 2021-10-16T21:13:26+0000

Answer:

$arc\ RF=80^o$

Explanation:

we know that

The inscribed angle is half that of the arc it comprises.

step 1

Find the measure of the arc PQR

$109^o=(1)/(2)[arc\ PQR]$

$arc\ PQR=218^o$

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

$112^o=(1)/(2)[arc\ QRF]$

$arc\ QRF=224^o$

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

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

$arc\ RF=80^o$