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
[tex] 150+73+x+65=360
\\
288+x =360
\\
x =360-288=72 [/tex]
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
[tex] m \ PQR = 72 +65 = 137 [/tex]
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
[tex] PQR= 6.48*2.39=15.5 inches [/tex]
