Question

identifying angle relationships of parallel lines
in the diagram, ( m parallel n ) and ( m ) and ( n ) are cut by transversal ( p ). which angle pairs are congruent? check all that apply.
( angle 1 ) and ( angle 5 )
( angle 3 ) and ( angle 8 )
( angle 6 ) and ( angle 4 )
( angle 8 ) and ( angle 2 )
( angle 4 ) and ( angle 7 )

Explanation:

Step1: Recall corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle1$ and $\angle5$ are corresponding angles.

Step2: Recall alternate - exterior and alternate - interior angles

Alternate - exterior angles: $\angle8$ and $\angle2$ are alternate - exterior angles. Alternate - interior angles: $\angle6$ and $\angle4$ are alternate - interior angles.

Step3: Check other pairs

For $\angle3$ and $\angle8$: $\angle3+\angle4 = 180^{\circ}$ (linear pair), $\angle4=\angle6$ (alternate - interior angles), $\angle6+\angle8 = 180^{\circ}$ (linear pair). So $\angle3
eq\angle8$. For $\angle4$ and $\angle7$: $\angle4=\angle6$ (alternate - interior angles), $\angle6+\angle7 = 180^{\circ}$ (linear pair). So $\angle4
eq\angle7$.

Answer:

$\angle1$ and $\angle5$, $\angle6$ and $\angle4$, $\angle8$ and $\angle2$