When a transversal intersects two parallel lines, certain angle relationships hold true, specifically alternate interior angles and corresponding angles.
Given:
- The angle at the intersection of line \(b\) and transversal \(a\) is \(50^\circ\) (let’s denote this angle as \( \angle 1 \)).
- The angle at the intersection of line \(c\) and transversal \(a\) at the top left is \(y\) degrees (let’s denote this angle as \( \angle 2 \)).
Since lines \(b\) and \(c\) are parallel, we can analyze the angles formed:
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The angle \( \angle 1 \) which is \(50^\circ\) is supplementary to the angle on the same side of the transversal, which is the top right angle at the intersection of line \(b\) and transversal \(a\) (let's denote it as \( \angle 3 \)): \[ \angle 1 + \angle 3 = 180^\circ \] Thus, \[ 50^\circ + \angle 3 = 180^\circ \implies \angle 3 = 130^\circ \]
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The angle \( \angle 3 \) is the corresponding angle to \( \angle 2 \) at the intersection of line \(c\) and transversal \(a\). Corresponding angles are equal when two parallel lines are cut by a transversal. Therefore, \[ \angle 2 = \angle 3 = 130^\circ \] So, \(y = 130\).
Thus, the value of \(y\) is: \[ \boxed{130} \]