y = 75
Solution:
In a straight line, sum of the adjacent angles = 180°
80° + m∠DGF = 180°
Subtract 80° from both sides of the equation.
m∠DGF = 100°
Sum of all the interior angles in a quadrilateral = 360°
m∠DGF + m∠GFE + m∠FED + m∠EDG = 360°
100° + 120° + 65° + y° = 360°
285° + y° = 360°
Subtract 285° from both sides, we get
y° = 75°
Hence the value of y is 75.