First we need to find the measurement of arc PQ.
And sum of measurement of all arc angles is 360 degree.
Let measurement of arc PQ is x degree.
Therefore, we get
![150+73+x+65=360 \\ 288+x =360 \\ x =360-288=72](https://img.qammunity.org/2019/formulas/mathematics/middle-school/u986i36z1hfu3bqc7thhfgtchq8gedgioj.png)
So measurement of arc PQ is 72.
And measurement of arc PQR is the sum of the measurement of arc PQ and QR.
That is
![m \ PQR = 72 +65 = 137](https://img.qammunity.org/2019/formulas/mathematics/middle-school/myncw7xso2vxaita0h28umc26dsglg4t2p.png)
measurement of Arc PQR = 137 degree= 2.39 radian
And radius is 6.48 inches
And arc length is the product of radius and central angle in radians .
That is
![PQR= 6.48*2.39=15.5 inches](https://img.qammunity.org/2019/formulas/mathematics/middle-school/our7cymispmx8dw3y2wt3x6tl9w5s0l39b.png)