Question

identifying types of angle relationships
lines ( m ) and ( n ) are cut by transversal ( l ).
which angle relationships are correct? choose three correct answers
( angle 5 ) and ( angle 7 ) are vertical angles.
( angle 2 ) and ( angle 8 ) are corresponding angles.
( angle 4 ) and ( angle 6 ) are same side interior angles.
( angle 3 ) and ( angle 6 ) are alternate interior angles.
( angle 1 ) and ( angle 8 ) are alternate exterior angles.

Explanation:

Step1: Analyze vertical angles

Vertical angles are opposite angles formed by two intersecting lines. $\angle5$ and $\angle7$ are opposite angles formed by the intersection of line $l$ and line $n$, so $\angle5$ and $\angle7$ are vertical angles.

Step2: Analyze corresponding angles

Corresponding angles are in the same relative position. $\angle2$ and $\angle8$ are not in the same relative position (corresponding angles should be in a “F - like” position). $\angle2$ and $\angle6$ are corresponding angles.

Step3: Analyze same - side interior angles

Same - side interior angles are between the two lines and on the same side of the transversal. $\angle4$ and $\angle6$ are between lines $m$ and $n$ and on the same side of transversal $l$, so $\angle4$ and $\angle6$ are same - side interior angles.

Step4: Analyze alternate interior angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. $\angle3$ and $\angle6$ are not alternate interior angles. $\angle4$ and $\angle6$ are same - side interior angles, $\angle3$ and $\angle6$ do not meet the criteria. $\angle4$ and $\angle5$ are alternate interior angles.

Step5: Analyze alternate exterior angles

Alternate exterior angles are outside the two lines and on opposite sides of the transversal. $\angle1$ and $\angle8$ are not alternate exterior angles. $\angle1$ and $\angle7$ are alternate exterior angles.

Answer:

$\angle5$ and $\angle7$ are vertical angles; $\angle4$ and $\angle6$ are same - side interior angles.