Question

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

Explanation:

Step1: Recall the definitions of angle pairs

• Alternate Exterior Angles: Non - adjacent angles that lie outside the two lines and on opposite sides of the transversal.
• Consecutive Interior Angles: Angles that lie between the two lines and on the same side of the transversal.
• Vertical Angles: Opposite angles formed by the intersection of two lines.
• Linear Pair: Adjacent angles that form a straight line (sum to \(180^{\circ}\)).
• Alternate Interior Angles: Non - adjacent angles that lie between the two lines and on opposite sides of the transversal.
• Corresponding Angles: Angles in the same relative position with respect to the two lines and the transversal.

Step2: Analyze each pair

• For \(\angle1\) and \(\angle7\):
• \(\angle1\) is outside line \(l\) and \(\angle7\) is outside line \(m\), and they are on opposite sides of the transversal \(t\). So, \(\angle1\) and \(\angle7\) are Alternate Exterior Angles.
• For \(\angle4\) and \(\angle6\):
• \(\angle4\) and \(\angle6\) lie between lines \(l\) and \(m\) and on opposite sides of the transversal \(t\). So, \(\angle4\) and \(\angle6\) are Alternate Interior Angles.
• For \(\angle5\) and \(\angle7\):
• \(\angle5\) and \(\angle7\) are opposite angles formed by the intersection of line \(m\) and transversal \(t\). So, \(\angle5\) and \(\angle7\) are Vertical Angles.
• For \(\angle1\) and \(\angle2\):
• \(\angle1\) and \(\angle2\) are adjacent angles that form a straight line (sum to \(180^{\circ}\)). So, \(\angle1\) and \(\angle2\) are a Linear Pair.
• For \(\angle6\) and \(\angle2\):
• \(\angle6\) and \(\angle2\) are in the same relative position with respect to lines \(l\), \(m\) and transversal \(t\). So, \(\angle6\) and \(\angle2\) are Corresponding Angles.
• For \(\angle4\) and \(\angle5\):
• \(\angle4\) and \(\angle5\) lie between lines \(l\) and \(m\) and on the same side of the transversal \(t\). So, \(\angle4\) and \(\angle5\) are Consecutive Interior Angles.

Answer:

• \(\angle1\) and \(\angle7\): Alternate Exterior Angles
• \(\angle4\) and \(\angle6\): Alternate Interior Angles
• \(\angle5\) and \(\angle7\): Vertical Angles
• \(\angle1\) and \(\angle2\): Linear Pair
• \(\angle6\) and \(\angle2\): Corresponding Angles
• \(\angle4\) and \(\angle5\): Consecutive Interior Angles