Find the length of arc PQ. Round to the nearest tenth.

Answer:The length of arc PQ to the nearest tenth is 8.1 inches.Step-by-step explanation:Let the measure of arc PQ be 'x'.Given:The measure of arc SR = 150°The measure of arc QR = 65°The measure of arc PS = 73°Radius of the circle is, [tex]R=6.48\ in[/tex]Sum of the measures of all arcs in a circle is always 360°. Therefore,Arc PQ + Arc QR + Arc SR + Arc PS = 360°[tex]x+65+150+73=360\\x+288=360\\x=360-288=72\°[/tex]Now, the arc length is given as:[tex]\textrm{Arc length}=R\theta\\Where\ \theta\rightarrow arc\ measure\ in\ radians[/tex]Now, measure of arc PQ, [tex]\theta=72\°=72\times \frac{\pi}{180}=0.4\pi[/tex]Therefore, arc length PQ = [tex]6.48\times 0.4\pi=2.592\times 3.14=8.138\approx 8.1\ in[/tex]So, the length of arc PQ to the nearest tenth is 8.1 inches.