Answer:
103°
Step-by-step explanation:
[tex] m\angle DST = m\angle DCS = 80\degree.. (\angle 's \: in\: alternate \: segment) [/tex]
[tex] In\: \triangle DST[/tex]
[tex] m\angle DTS = 180\degree - (60\degree + 80\degree) [/tex]
[tex] m\angle DTS = 180\degree - 140\degree[/tex]
[tex] m\angle DTS = 40\degree[/tex]
[tex] m\angle ETA+m\angle ETD+ m\angle DTS= 180\degree.. (straight \:line \:\angle 's) [/tex]
[tex] m\angle ETA+37\degree + 40\degree = 180\degree[/tex]
[tex] m\angle ETA+77\degree = 180\degree[/tex]
[tex] m\angle ETA = 180\degree-77\degree [/tex]
[tex] m\angle ETA = 103\degree [/tex]
[tex] x = m\angle ETA = 103\degree.(\angle 's \: in\: alternate \: segment) [/tex]
