Question

what is the measure of \\( \angle 7 \\)?

Explanation:

Step1: Find the measure of ∠4

Since ∠4 and the \(137^{\circ}\) angle are supplementary (they form a linear - pair), we use the formula \(\angle4 + 137^{\circ}=180^{\circ}\).
So, \(\angle4=180^{\circ}- 137^{\circ}=43^{\circ}\).

Step2: Use the property of corresponding angles

Assume lines \(u\) and \(t\) are parallel (by the nature of angle - relationship problems in this format). \(\angle7\) and \(\angle4\) are corresponding angles.
By the corresponding angles postulate (if two parallel lines are cut by a transversal, then corresponding angles are equal), \(\angle7=\angle4\).

Answer:

\(43^{\circ}\) (Option C)