In the figure below, AA’ is parallel to CC’. The measure w of ∠A′AB is equal to 135 degrees and the measure z of ∠C′CB is equal to 147 degrees. Find ∠ABC .

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100 degrees

78 degrees

80 degrees

40 degrees

answer is B.

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Detailed Solution

We have w = 135 degrees = ∠A′AB and z = 147 degrees = ∠C′CB and AA’ is parallel to CC’. We will draw a line BB’ parallel to both AA’ and CC’ in between.
Question Image

Here we have ∠A′AB as the alternate interior angle to ∠ABB′ when AA’ is parallel to BB’.
We also have ∠C′CB as the alternate interior angle to ∠B′BC when CC’ is parallel to BB’.
It is clear from the figure that

Since we know that the sum of alternate interior angle is 180 degrees for a transversal, we can write relations as

degrees

degrees
So as we know ∠A′AB = 135 degrees, we have

degrees

As we know∠C′CB = 147 degrees, we have

degrees

We had already formed the relation,

, so we have

So, the correct ans is “Option 2”.

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