Because they are vertical angles, angle a is equal to angle d.
Because they add to form a straight line: a + b + f = 180.
Substitute d for a to yield: (d) + b + f = 180. Substitute 150 for b + f to yield: d + (150) = 180. Thus, d = 180 − 150 = 30.
Because x° and 20° are supplementary, x = 180 − 20 = 160. Because y° and 20° are vertical, y = 20. So x − y = 160 − 20 = 140.
c and d are vertical angles, therefore, they are equal. Because they sum to 200, each must be 100. a + b = c, because c is an exterior angle of the triangle shown, and a and b are the two non-adjacent interior angles. a + b = c = 100.
In a system of parallel lines cut by a transversal, opposite exterior angles (like a and g) are equal. g = a = 120.
From question 4, you know that a = 120. Because a = 120, its supplementary angle d = 180 − 120 = 60. Because a + b + c + d = 360, and d = 60, then a + b + c = 300.