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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.

Parallel lines a, b, and c are cut by a pipe cleaner transversal. All angles are described clockwise, from uppercase left. Where line a intersects with the pipe cleaner, the angles are: 1, 2, 4, 3. Where line b intersects with the pipe cleaner, the angles are 5, 6, 8, 7. Where line c intersects with the pipe cleaner, the angles are: 9, 130 degrees, 12, 11.
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°.

1 answer

To analyze the relationship between the angle of 130° and angle 3, we first need to identify their positions in relation to the parallel lines and the transversal.

  1. Angles at line c (where the angle of 130° is located):
    The angles at line c are labeled as 9, 130°, 12, and 11.

  2. Angles at line a (where angle 3 is found):
    The angles at line a are labeled as 1, 2, 4, and 3.

Now we will determine how angle 3 relates to the 130° angle.

  • Same-side interior angles: These are angles on the same side of the transversal and between the two parallel lines. Angle 3 and the 130° angle are not on the same side. They are in fact on opposite lines.

  • Alternate interior angles: These are angles located between the parallel lines but on opposite sides of the transversal. Angle 3 and the 130° angle are not alternate interior angles, as they do not share the same position with respect to the parallel lines and the transversal.

  • Corresponding angles: These are angles that are in the same position relative to the parallel lines and the transversal. In this case, angle 3 and the 130° angle are in different positions, so they are not corresponding angles.

  • Alternate exterior angles: These are angles located outside the parallel lines and on opposite sides of the transversal. Angle 3 is below line a, while the 130° angle is above line c. Therefore, these angles are not alternate exterior angles either.

Given that we need to figure out the relation between angle 3 and the angle of 130°, we can conclude:

Since the angles 130° and angle 3 are in different positions and on opposite sides of the transversal, they cannot be same-side interior angles, alternate interior angles, corresponding angles, or alternate exterior angles. The only relevant relationship is that they are supplementary.

Thus, the true statement concerning angle 3 would be that if the 130° angle is on one side of the transversal and angle 3 is on the other side, angle 3 must be supplementary to the 130° angle:

The true statement is that angle 3 measures 50° since 130° + angle 3 = 180° (they are same-side interior angles).