Question

letters a, b, c, and d are angle measures. which should equal 105° to prove that f || g? d b c a

Explanation:

Step1: Find the measure of \(a\) and \(b\)

Since \(a\) and \(75^{\circ}\) are vertical angles, \(a = 75^{\circ}\). And \(a + b=180^{\circ}\) (linear - pair), so \(b = 180^{\circ}-75^{\circ}=105^{\circ}\).

Step2: Use the property of parallel lines

If \(b = 105^{\circ}\), then by the converse of the same - side interior angles theorem (if the sum of same - side interior angles is \(180^{\circ}\), the lines are parallel), we can prove \(f\parallel g\).

Answer:

\(b\)