In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circ

When I see this figure, I don't see circles and chords - I see a polygon. Had it been about circles and chords, there would have been 1 or 2 chords. These all are making a complete polygon inscribed in the circle.
We are given exterior angles of a polygon. I know that the sum of all exterior angles will be 360.
Consider the side a. It is turned 40 degrees to get side b. Side b is turned 35 degrees to get side c and so on...
When are 2 lines parallel? When a side is eventually turned 180 degrees, it will have the same slope as before.

I notice the figures 32, 32 and 36. They are different from the rest which end in a 5 or a 0. I am thinking that if one of them is a part of my sum of 180, all 3 need to be so add up to 100. Fortunately I have a 45 degrees angle between them and a 35 degrees angle after them.
This tells me that side e is turned 180 degrees clockwise to get side j (32 + 36 + 45 + 32 + 35)

So sides e and j are parallel

Answer (E)

Chords e and j are parallel to each other & Option (E) is correct.

For two chords to be parallel they need to have 180 degree separation in alignment. The figure gives us the difference between two chords, so we must find the correct chords between whom a total of 180 deg separation is present.

Chord e + ( 40 + 35 + 35 + 40 + 30 ) = Chord J. In the anticlockwise direction

Chord e + 180 deg = Chord j.

Hence they are parallel and Option (E) is our choice.

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We need the angles on one side to add to 180 and the angles on the other side to add to 180.

(Notice that we just rotate one space clockwise with each answer choice, so we can just drop the last item off each list and add the new number to the front.)
A) We have units digits of 0, 5, 2, 5, 6 on one side. That won't end in 0. Eliminate.
B) We have units digits of 0, 0, 5, 2, 5 on one side. That won't end in 0. Eliminate.
C) We have units digits of 5, 0, 0, 5, 2 on one side. That won't end in 0. Eliminate.
D) We have units digits of 5, 5, 0, 0, 5 on one side. That won't end in 0. Eliminate.
E)

Answer choice E.

chetan2u sorry to bug again but your approach

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VeritasKarishma Your thoughts please !!
Any quicker way to do this .

Just start adding the respective angles.

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