Question

use the figure below to match the type of angles with the correct angles.<1 and <3choose<1 and <choose<4 and <same-side exterior anglescorresponding anglessame-side interior anglescomplementaryalternate interior anglesalternate exterior anglesvertical anglessupplementary<5 and <8choose<6 and <8choose<3 and <5choose<4 and <5choose

Explanation:

Step1: Recall angle definitions

• Vertical Angles: Angles opposite each other when two lines intersect.
• Supplementary Angles: Two angles whose sum is \(180^{\circ}\).
• Alternate Interior Angles: Angles between two lines and on opposite sides of a transversal.
• Same - Side Interior Angles: Angles between two lines and on the same side of a transversal.
• Corresponding Angles: Angles in matching positions relative to the lines and transversal.
• Alternate Exterior Angles: Angles outside the two lines and on opposite sides of the transversal.
• Same - Side Exterior Angles: Angles outside the two lines and on the same side of the transversal.
• Complementary Angles: Two angles whose sum is \(90^{\circ}\).

Step2: Analyze \(\angle1\) and \(\angle3\)

\(\angle1\) and \(\angle3\) are adjacent and form a linear pair. Their sum is \(180^{\circ}\), so they are Supplementary.

Step3: Analyze \(\angle5\) and \(\angle8\)

\(\angle5\) and \(\angle8\) are opposite each other when two lines intersect. So they are Vertical Angles.

Step4: Analyze \(\angle6\) and \(\angle8\)

\(\angle6\) and \(\angle8\) are adjacent and form a linear pair. Their sum is \(180^{\circ}\), so they are Supplementary.

Step5: Analyze \(\angle3\) and \(\angle5\)

\(\angle3\) and \(\angle5\) are between the two lines \(m\) and \(l\) and on opposite sides of the transversal \(n\). So they are Alternate Interior Angles.

Step6: Analyze \(\angle4\) and \(\angle5\)

\(\angle4\) and \(\angle5\) are between the two lines \(m\) and \(l\) and on the same side of the transversal \(n\). So they are Same - Side Interior Angles.

Answer:

\(\angle1\) and \(\angle3\): Supplementary
\(\angle5\) and \(\angle8\): Vertical Angles
\(\angle6\) and \(\angle8\): Supplementary
\(\angle3\) and \(\angle5\): Alternate Interior Angles
\(\angle4\) and \(\angle5\): Same - Side Interior Angles