Consider the following figure: If \(l_1 \parallel l_2\) and \(l_3 \parallel l_4\), then which one of the following relations is correct?
\(2Y^\circ + x^\circ = 180^\circ\)
When a transversal cuts two parallel lines, the interior angles on the same side of the transversal are supplementary, that is, they add up to 180 degrees.
In this figure, the two angles marked Y degrees are formed at intersections involving the parallel line pairs, while x degrees is formed at another related intersection using the same parallel-line properties.
Applying the co-interior angle relationships between the two pairs of parallel lines gives the relation 2Y° + x° = 180°.
Hence, the correct answer is 2Y° + x° = 180°.
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