Question

match the following
∠3 and ∠5
∠5 and ∠4
∠1 and ∠4
∠1 and ∠7
vertical angles
consecutive exterior angles
consecutive interior angles
alternate interior angles

Explanation:

To solve this angle - matching problem, we need to recall the definitions of different types of angles formed by parallel lines and a transversal:

1. Vertical Angles: These are pairs of opposite angles formed by the intersection of two lines. They are equal in measure. For example, if two lines intersect, the angles opposite each other are vertical angles.
2. Consecutive Exterior Angles: These are two exterior angles that lie on the same side of the transversal and outside the two lines.
3. Consecutive Interior Angles: These are two interior angles that lie on the same side of the transversal and between the two lines. They are also known as same - side interior angles.
4. Alternate Interior Angles: These are two non - adjacent interior angles that lie on opposite sides of the transversal and between the two lines.

Now let's match each pair of angles:

• $\angle3$ and $\angle5$: These are vertical angles because they are opposite each other when two lines intersect.
• $\angle5$ and $\angle4$: These are consecutive interior angles. They lie on the same side of the transversal and between the two lines (assuming the lines are parallel and cut by a transversal).
• $\angle1$ and $\angle4$: These are alternate interior angles. They lie on opposite sides of the transversal and between the two lines.
• $\angle1$ and $\angle7$: These are consecutive exterior angles. They lie on the same side of the transversal and outside the two lines.

Answer:

• $\angle3$ and $\angle5$: Vertical Angles
• $\angle5$ and $\angle4$: Consecutive Interior Angles
• $\angle1$ and $\angle4$: Alternate Interior Angles
• $\angle1$ and $\angle7$: Consecutive Exterior Angles