Question 1

Find the unknown angle x.

Question 2

Answer:

103°

Explanation:

$m\angle DST = m\angle DCS = 80\degree.. (\angle 's \: in\: alternate \: segment)$

$In\: \triangle DST$

$m\angle DTS = 180\degree - (60\degree + 80\degree)$

$m\angle DTS = 180\degree - 140\degree$

$m\angle DTS = 40\degree$

$m\angle ETA+m\angle ETD+ m\angle DTS= 180\degree.. (straight \:line \:\angle 's)$

$m\angle ETA+37\degree + 40\degree = 180\degree$

$m\angle ETA+77\degree = 180\degree$

$m\angle ETA = 180\degree-77\degree$

$m\angle ETA = 103\degree$

$x = m\angle ETA = 103\degree.(\angle 's \: in\: alternate \: segment)$

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