Question

match the angles with their type. $\angle 7$ and $\angle 2$ $\angle 3$ and $\angle 7$ $\angle 6$ and $\angle 4$ $\angle 5$ and $\angle 4$ corresponding angles alternate interior angles alternate exterior angle consecutive interior angles

Explanation:

Step1: Recall angle - type definitions

• Corresponding angles: Angles that are in the same relative position.
• Alternate interior angles: Angles that lie between two lines and on opposite sides of a transversal.
• Alternate exterior angles: Angles that lie outside two lines and on opposite sides of a transversal.
• Consecutive interior angles: Angles that lie between two lines and on the same side of a transversal.

Step2: Analyze \(\angle7\) and \(\angle2\)

\(\angle7\) and \(\angle2\) are in the same relative position. So, \(\angle7\) and \(\angle2\) are corresponding angles.

Step3: Analyze \(\angle3\) and \(\angle7\)

\(\angle3\) and \(\angle7\) lie outside the two lines \(l\) and \(m\) and on opposite sides of the transversal \(t\). So, \(\angle3\) and \(\angle7\) are alternate exterior angles.

Step4: Analyze \(\angle6\) and \(\angle4\)

\(\angle6\) and \(\angle4\) lie between the two lines \(l\) and \(m\) and on opposite sides of the transversal \(t\). So, \(\angle6\) and \(\angle4\) are alternate interior angles.

Step5: Analyze \(\angle5\) and \(\angle4\)

\(\angle5\) and \(\angle4\) lie between the two lines \(l\) and \(m\) and on the same side of the transversal \(t\). So, \(\angle5\) and \(\angle4\) are consecutive interior angles.

Answer:

\(\angle7\) and \(\angle2\): corresponding angles; \(\angle3\) and \(\angle7\): alternate exterior angles; \(\angle6\) and \(\angle4\): alternate interior angles; \(\angle5\) and \(\angle4\): consecutive interior angles.