Question

<4 and <6
<3 and <6
<1 and <7
<2 and <7
<1 and <5
<5 and <8
<6 and <8
<3 and <5
<4 and <5
<1 and <8
<2 and <6
<4 and <8
<3 and <7

Explanation:

Step1: Recall angle - pair definitions

• Alternate exterior angles: Two angles that lie outside the two lines and on opposite sides of the transversal.
• Corresponding angles: Two angles that are in the same relative position with respect to the two lines and the transversal.
• Vertical angles: Two non - adjacent angles formed by the intersection of two lines.
• Supplementary angles: Two angles whose sum is \(180^{\circ}\).
• Alternate interior angles: Two angles that lie between the two lines and on opposite sides of the transversal.
• Same - side interior angles: Two angles that lie between the two lines and on the same side of the transversal.

Step2: Analyze each pair

• For \(\angle2\) and \(\angle7\):
• \(\angle2\) and \(\angle7\) are alternate exterior angles.
• For \(\angle1\) and \(\angle5\):
• \(\angle1\) and \(\angle5\) are corresponding angles.
• For \(\angle5\) and \(\angle8\):
• \(\angle5\) and \(\angle8\) are vertical angles.
• For \(\angle6\) and \(\angle8\):
• \(\angle6\) and \(\angle8\) are supplementary angles (\(\angle6+\angle8 = 180^{\circ}\) if we assume the lines are parallel and use the linear - pair property).
• For \(\angle3\) and \(\angle5\):
• \(\angle3\) and \(\angle5\) are same - side interior angles.
• For \(\angle4\) and \(\angle5\):
• \(\angle4\) and \(\angle5\) are supplementary angles (\(\angle4+\angle5=180^{\circ}\) as they form a linear pair).
• For \(\angle1\) and \(\angle8\):
• \(\angle1\) and \(\angle8\) are alternate exterior angles.
• For \(\angle2\) and \(\angle6\):
• \(\angle2\) and \(\angle6\) are alternate interior angles.
• For \(\angle4\) and \(\angle8\):
• \(\angle4\) and \(\angle8\) are corresponding angles.
• For \(\angle3\) and \(\angle7\):
• \(\angle3\) and \(\angle7\) are corresponding angles.

Answer:

\(\angle2\) and \(\angle7\): Alternate Exterior; \(\angle1\) and \(\angle5\): Corresponding; \(\angle5\) and \(\angle8\): Vertical; \(\angle6\) and \(\angle8\): Supplementary; \(\angle3\) and \(\angle5\): Same - Side Interior; \(\angle4\) and \(\angle5\): Supplementary; \(\angle1\) and \(\angle8\): Alternate Exterior; \(\angle2\) and \(\angle6\): Alternate Interior; \(\angle4\) and \(\angle8\): Corresponding; \(\angle3\) and \(\angle7\): Corresponding.