Explanation:
2 lines are parallel in this context, if they have the same interception angles with a shared intercepting line.
a)
the lines a and b are parallel.
on line a : 37° and the angle right above it are a linear pair. that means together they have 180°.
180 = 37 + angle above
angle above = 180 - 37 = 143°
and the same applies to line b and the angle 143°. it creates a linear pair with the angle right above it, which is 37°.
so, the interception angles are the same, and both lines are parallel.
b)
not parallel.
the angle diametrically opposite from the 60° angle at the same intersection must be also 60°.
if the lines a and b are parallel, then this angle must be the same as the one marked with 120°. so, they are not the same angles, so, the lines are not parallel.
c)
not parallel.
the angle directly left of the 50° angle forms Anson a linear pair of angles (together 180°). so, the left angle is 180 - 50 = 130°. and for the lines x and y to be parallel, this angle must be the same as the one marked with 140°. so, the intercepting angles are different, which means the lines are not parallel.
d)
not parallel.
to be parallel the right upper angle at the s/r interception must be also 50° as its corresponding angle at s/q.
and then its vertical angle must be also 50°, and not 130°.
so, the interception angles are not the same.
e)
the lines m and n are parallel.
the linear pair angle to the 50° angle downwards is 130°.
its corresponding angle at line n must be the same to be parallel. and it is (130°).
so, the lines are parallel.
f)
we don't know. so, in general, they are not parallel.
the given 2 angles are only for the intersection with one line. we know nothing about the intersecting angles with the second line. so, it can be at any angle.
therefore in general, not parallel.
g)
lines a and s are parallel.
the given angles are 90°. so, their linear paired and then corresponding angles must all be 90° too.
so, the angles are the same. that means the lines are parallel.
h)
like f), we don't know. so, in general, they are not parallel.
the given 2 angles are only for the intersection with one line. we know nothing about the intersecting angles with the second line. so, it can be at any angle.
therefore in general, not parallel.
i)
not parallel.
as the vertical corresponding angles 70° and the sum of 80° and 30° would have to be the same for the lines to be parallel, but 70 is different to 110.
so, the intersecting angles are different, and the lines are not parallel.