<p>You can actually answer the problem just by noticing that, if the two lines were parallel, the value of x would already be defined and would be, therefore, unique. So, the answer must be A, which is the only alternative that presents only one value that x cannot take.</p>
<p>In the fomal way, for the lines to be parallel, the corresponding angles ABC and DC’down’ must be equal, that is, DC’down’ = x+40°. As DC’down’ + DCB = 180° –>
(x+40°) + (2x+20°) = 180° –> x=40°. As we want non-parallel lines, we must have x#40°</p>
<p>If it did, the angles would be 80 and 100, which are supplementary. They can’t be supplementary because the lines aren’t parallel. Therefore, it is a true statement.</p>
<p>It’s actually not F. Although they cannot be equal to 40 degrees, there are other angle measures they could be to be parallel. For example, they could both be 90 degrees, 89 and 91, 88 and 92 and so on. Therefore, K would have to be the correct answer.</p>