Question

3 which angles would the consecutive interior angles theorem state are supplementary?
∠1 and ∠5, ∠3 and ∠7
∠2 and ∠4; ∠6 and ∠8
∠3 and ∠5, ∠4 and ∠6
∠1 and ∠8; ∠2 and ∠7

Explanation:

Step1: Recall the definition of consecutive interior angles

Consecutive interior angles are two angles that lie between two lines and on the same side of a transversal. When the two lines are parallel, consecutive interior angles are supplementary.

Step2: Analyze each option

• Option 1: $\angle1$ and $\angle5$, $\angle3$ and $\angle7$ are corresponding angles.
• Option 2: $\angle2$ and $\angle4$, $\angle6$ and $\angle8$ are vertical angles.
• Option 3: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$ are consecutive interior angles.
• Option 4: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$ are alternate exterior angles.

Answer:

$\angle3$ and $\angle5$, $\angle4$ and $\angle6$ (the third option)