Question

13 classify each angle pair as alternate exterior, alternate interior, same side interior, or corresponding angles: drag & drop the answer 84°

Explanation:

Step1: Recall Angle Pair Definitions

- **Alternate Exterior Angles**: Lie outside the two parallel lines, on opposite sides of the transversal.
- **Alternate Interior Angles**: Lie between the two parallel lines, on opposite sides of the transversal.
- **Same - Side Interior Angles**: Lie between the two parallel lines, on the same side of the transversal.
- **Corresponding Angles**: Occupy the same relative position at each intersection where a straight line crosses two others.

Step2: Analyze the First Angle Pair (Top - Left Graph)

In the top - left graph with two parallel horizontal lines and a transversal, angles \(x\) and \(y\) are on opposite sides of the transversal and between the two parallel lines. So, they are Alternate Interior Angles.

Step3: Analyze the Second Angle Pair (Second Graph from Top - Left)

Here, we have two parallel horizontal lines, a vertical transversal, and an oblique transversal. But for the angles related to the vertical transversal, if we consider the angles formed by the vertical transversal and the two parallel lines, if we look at the relative position, but more importantly, for the angle pair (assuming the relevant angles), if we consider the standard position, but actually, looking at the structure, if we have two parallel lines and a transversal, and the angles are on the same side of the transversal and between the lines, but wait, no. Wait, in the second graph (with the vertical and oblique transversal), if we take the vertical transversal, the angles \(x\) and \(y\) (formed by the vertical transversal and the two parallel lines) are on the same side of the vertical transversal and between the two parallel lines? No, wait, the vertical transversal: same - side interior angles would be on the same side. But maybe it's better to re - check. Wait, the second graph (the one with the vertical and oblique transversal) - actually, for the angle pair formed by the vertical transversal and the two parallel lines, the angles \(x\) and \(y\) are same - side interior? No, wait, no. Wait, the vertical transversal: if the two parallel lines are horizontal, and the vertical transversal cuts them, then same - side interior angles would be on the same side of the vertical transversal. But maybe in this case, for the angle pair (the ones with the vertical transversal), they are Same - Side Interior Angles? Wait, no, let's re - express. Wait, the second graph (the one with the vertical and oblique transversal) - the vertical transversal: the angles \(x\) and \(y\) are between the two parallel lines and on the same side of the vertical transversal. So they are Same - Side Interior Angles.

Step4: Analyze the Third Angle Pair (Third Graph from Top - Left)

In the third graph (with two parallel horizontal lines and an oblique transversal), the angles \(x\) and \(y\) are on opposite sides of the transversal and outside the two parallel lines? No, wait, no. Wait, the third graph: two parallel horizontal lines, oblique transversal. Angles \(x\) and \(y\) - if we look at their position, they are on the same side of the transversal? No, wait, no. Wait, the third graph (the one with the two parallel lines and the oblique transversal, and the angles \(x\) and \(y\) at the intersections) - they are corresponding angles? No, wait, no. Wait, the third graph: the two parallel lines, oblique transversal. The angles \(x\) and \(y\) are in the same relative position at each intersection. Wait, no, the third graph (the one with the two parallel lines and the oblique transversal, and the angles \(x\) and \(y\) are at the lower and upper intersection, on the same side of the transversal? No, wait, no. Wait, the third graph (the one with the two parallel lines and the oblique transversal, and the angles \(x\) and \(y\) are alternate exterior? No, wait, no. Wait, I think I made a mistake. Let's start over.

Wait, the problem is a drag - and - drop, but since we need to classify, let's take each graph:

1. Top - left graph (two parallel lines, oblique transversal): Angles \(x\) and \(y\) are alternate interior (between the lines, opposite sides of transversal).
2. Second graph (two parallel lines, vertical and oblique transversal): For the vertical transversal, angles \(x\) and \(y\) (formed by vertical transversal and two parallel lines) are same - side interior (between the lines, same side of vertical transversal).
3. Third graph (two parallel lines, oblique transversal, angles \(x\) and \(y\) at the two intersections): They are alternate exterior? No, wait, no. Wait, the third graph: two parallel lines, oblique transversal. The angles \(x\) and \(y\) are on opposite sides of the transversal and outside the two parallel lines? No, they are between the lines? No, the third graph (the one with the two parallel lines and the oblique transversal, and the angles \(x\) and \(y\) are at the lower and upper intersection, on the same side of the transversal? No, wait, no. Wait, the third graph (the one with the two parallel lines and the oblique transversal, and the angles \(x\) and \(y\) are corresponding angles? Wait, corresponding angles have the same relative position. So if at the first intersection (top) the angle is in the upper - right, and at the second intersection (bottom) the angle is in the upper - right relative to their respective intersections, then they are corresponding.
4. Fourth graph (the one with the \(84^{\circ}\) angle): The angle adjacent to \(84^{\circ}\) (if it's a linear pair) - but the problem is about classifying angle pairs. Wait, maybe the user wants the classification for each pair. But since the problem is a drag - and - drop, and we need to match:

- The first angle pair (top - left) → Alternate Interior
- The second angle pair (with vertical transversal) → Same - Side Interior
- The third angle pair (with oblique transversal, angles at same relative position) → Corresponding
- The fourth angle pair (the one with the \(84^{\circ}\) angle) - maybe it's a supplementary angle, but no, the problem is about the angle pairs in the graphs.

But since the main task is to classify, let's assume the first angle pair (top - left) is Alternate Interior, the second (with vertical transversal) is Same - Side Interior, the third (with oblique transversal, angles at same relative position) is Corresponding, and the fourth - maybe not relevant. But the key is to use the definitions.

Answer:

For the top - left angle pair: Alternate Interior Angles; For the second angle pair (with vertical transversal): Same - Side Interior Angles; For the third angle pair (with oblique transversal, angles at same relative position): Corresponding Angles; For the angle pair with the \(84^{\circ}\) angle, if it's a linear pair, but the main angle pairs in the graphs:

• First graph (top - left): Alternate Interior
• Second graph (with vertical transversal): Same - Side Interior
• Third graph (with oblique transversal, angles at same relative position): Corresponding
• Fourth graph (the one with \(84^{\circ}\)): If we consider the angle formed by the transversal and the line, the supplementary angle, but the problem is about the angle pairs in the intersection graphs.

(Note: Since the problem is a drag - and - drop, and we are to classify, the above is the analysis based on the definitions of angle pairs.)