Measure of arc XY

whats the measure of Arc XY if Major Arc =110 and angle XZY=39

 

I will assume that Z is the centre of the circle.

 

first draw the pic .

360-39=131 degrees

 

\(\frac{341}{360}\times 2*\pi*r=110\\ \frac{341\times 2*\pi}{360}*r=110\\ r=110*\frac{360}{341\times 2*\pi}\\ \)

 

110*360/(341*2*pi) = 18.4825095203491358 = 18.48 units

 

\(Arc \;XY=\frac{39}{360}*2\pi*18.48\\\)

 

39/360*2*pi*18.48 = 12.5789369849735321

 

\(Arc\;XY\approx12.58\;units\)