Question

a pipe cleaner lay across a wire shelf. the wires that make up the shelf are parallel, and the pipe cleaner is a transversal. the parallel wires are labeled a, b, and, c, and the angles are labeled with numbers. the measure of one angle is 130°. which statement is true regarding the 130° angle and angle 3? ○ they are same - side interior angles, so angle 3 measures 50°. ○ they are alternate interior angles, so angle 3 also measures 130°. ○ they are corresponding angles, so angle 3 also measures 130°. ○ they are alternate exterior angles, so angle 3 measures 50°.

Explanation:

1. Analyze the first option: Same - side interior angles are supplementary (sum to \(180^{\circ}\)). If one angle is \(130^{\circ}\), the other should be \(180 - 130=50^{\circ}\). But we need to check if angle 3 and the \(130^{\circ}\) angle are same - side interior angles. From the diagram, angle 3 and the \(130^{\circ}\) angle (let's assume the \(130^{\circ}\) angle is angle 12 or 10, but looking at the parallel lines a and c, and the transversal, angle 3 and the \(130^{\circ}\) angle: Wait, let's re - examine the angle relationships. Wait, the first option says they are same - side interior angles. Let's recall the properties:

• Same - side interior angles: When two parallel lines are cut by a transversal, same - side interior angles are supplementary. So if one is \(130^{\circ}\), the other is \(50^{\circ}\). But let's check the position of angle 3. Line a and line c are parallel, and the transversal is the pipe cleaner. Angle 3 is between line a and line b? Wait, no, the parallel lines are a, b, c. Wait, maybe the \(130^{\circ}\) angle and angle 3: Let's check the other options first.

1. Analyze the second option: Alternate interior angles are equal. But for alternate interior angles, the angles are on opposite sides of the transversal and inside the two parallel lines. Angle 3 is on line a - b region, and the \(130^{\circ}\) angle is on line c region. So they are not alternate interior angles.
2. Analyze the third option: Corresponding angles are equal. Corresponding angles are in the same position relative to the parallel lines and the transversal. Angle 3 and the \(130^{\circ}\) angle are not in corresponding positions.
3. Analyze the fourth option: Alternate exterior angles are equal. But the \(130^{\circ}\) angle and angle 3 are not exterior angles. Wait, maybe I made a mistake. Wait, let's re - look at the first option. The \(130^{\circ}\) angle and angle 3: If we consider lines a and c (parallel) and the transversal, angle 3 and the \(130^{\circ}\) angle are same - side interior angles. Since same - side interior angles are supplementary, if one is \(130^{\circ}\), the other (angle 3) is \(180 - 130 = 50^{\circ}\). So the first option is correct.

Answer:

They are same - side interior angles, so angle 3 measures \(50^{\circ}\).