Which lines are parallel? check all that apply.

a) b||f
b) b||d
c) c||e
d) c||d
e) d||f
g) e||f

Two lines will be parallel if when intersecting the same line, their angles in their respectable quadrants are equal. So all we have to do is figure out the same angle for each lines intersection. Since we have 5 lines that means we only solve 5 angles. i am going to find the angles in the top right corner of each intersection since that one is given for line b and i am going to label each angle alphabetically starting with b like this:
b = 89.5

Now now for c.we are given the opposite angle and at an Intersection opposite angles are equal so:
c= 91.5

for s we are given the angle on the same line. all lines add up to 180 degrers so the give angle and the angle we are searching for add up to 180.:
d + 89.5 = 180
d = 90.5

e follows same process as d so:
e + 88.5 = 180
e = 91.5

f can follow same as d and e so:
f + 90.5 =180
f = 89.5

Now we can pair up the lines with equal angles
b & f
c & e
d matches nothing so is not parallel

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