Question

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

Explanation:

Step1: Recall angle - pair relationships

When two lines are parallel, corresponding angles, alternate - interior angles, and alternate - exterior angles are equal, and same - side interior angles are supplementary. The angle of 75° and the angle we want to find are same - side interior angles.

Step2: Use the property of same - side interior angles

Same - side interior angles between two parallel lines are supplementary, i.e., their sum is 180°. Let the unknown angle be \(x\). We know that \(x + 75^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-75^{\circ}=105^{\circ}\). Angle \(a\) is the same - side interior angle to the 75° angle.

Answer:

A. \(a\)