Question

use the diagram below to identify the pairs of angles. match the appropriate name with the corresponding pair of angles.
∠7 and ∠10
∠9 and ∠12
∠5 and ∠11
∠5 and ∠7
∠10 and ∠8
∠8 and ∠12
∠6 and ∠11
vertical angles
consecutive (same side) exterior angles
alternate exterior angles
alternate interior angles
corresponding angles
linear pair
consecutive (same side) interior angles

Explanation:

Step1: Recall definitions

• Vertical Angles: Angles opposite each other when two lines cross.
• Alternate Exterior Angles: Non - adjacent exterior angles that lie on opposite sides of the transversal.
• Linear Pair: Adjacent angles that form a straight line (\(180^{\circ}\)).
• Consecutive (Same Side) Exterior Angles: Exterior angles that lie on the same side of the transversal.
• Alternate Interior Angles: Non - adjacent interior angles that lie on opposite sides of the transversal.
• Corresponding Angles: Angles in the same relative position.
• Consecutive (Same Side) Interior Angles: Interior angles that lie on the same side of the transversal.

Step2: Match each pair

• Vertical Angles: \(\angle5\) and \(\angle7\) (opposite each other when two lines cross).
• Consecutive (Same Side) Exterior Angles: \(\angle9\) and \(\angle12\) (exterior, same - side of transversal).
• Alternate Exterior Angles: \(\angle6\) and \(\angle11\) (exterior, opposite - side of transversal).
• Linear Pair: \(\angle8\) and \(\angle12\) (adjacent, form a straight line).
• Consecutive (Same Side) Interior Angles: \(\angle7\) and \(\angle10\) (interior, same - side of transversal).
• Alternate Interior Angles: \(\angle5\) and \(\angle11\) (interior, opposite - side of transversal).
• Corresponding Angles: \(\angle10\) and \(\angle8\) (same relative position).

Answer:

• \(\angle5\) and \(\angle7\): Vertical Angles
• \(\angle9\) and \(\angle12\): Consecutive (Same Side) Exterior Angles
• \(\angle6\) and \(\angle11\): Alternate Exterior Angles
• \(\angle8\) and \(\angle12\): Linear Pair
• \(\angle7\) and \(\angle10\): Consecutive (Same Side) Interior Angles
• \(\angle5\) and \(\angle11\): Alternate Interior Angles
• \(\angle10\) and \(\angle8\): Corresponding Angles