Answer: 77°
Step-by-step explanation:
[tex]\angle X = 85\ and\ \angle X=\dfrac{1}{2}\stackrel\frown{YFW}\\\\\rightarrow\ 85 =\dfrac{1}{2}\stackrel\frown{YFW}\\\\\rightarrow\ 170 =\ \stackrel\frown{YFW}\\\\\\\\\stackrel\frown{XY} + \stackrel\frown{YW}+\stackrel\frown{WX}\ =360\\\\100\ +\ 170\ +\stackrel\frown{WX}\ =360\\\\270\ +\stackrel\frown{WX}\ =360\\\\\stackrel\frown{WX}\ =90\\\\\\\\\stackrel\frown{FW}+\stackrel\frown{WX}=\stackrel\frown{FWX}\\ \\64+90=\stackrel\frown{FWX}\\\\154=\stackrel\frown{FWX}[/tex]
[tex]\angle Y=\dfrac{1}{2}\stackrel\frown{YWX}\\\\.\quad =\dfrac{1}{2}(154)\\\\.\quad =77[/tex]
