Question

5 what is the measure of \\( \angle 4 \\)?

Explanation:

Step1: Find the measure of ∠5

Since ∠5 and the \(100^{\circ}\) angle are supplementary (they form a linear pair), we use the formula \(\angle5 = 180^{\circ}-\angle8\).
\(\angle5=180^{\circ} - 100^{\circ}=80^{\circ}\)

Step2: Use the property of parallel lines and alternate interior angles

Lines \(e\) and \(f\) are parallel, and \(d\) is a transversal. \(\angle4\) and \(\angle5\) are alternate interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(\angle4=\angle5\)

Answer:

\(80^{\circ}\)