Question

identify two pairs of consecutive interior angles.
a. ∠4 and ∠7; ∠10 and ∠13
b. ∠4 and ∠16; ∠6 and ∠10
c. ∠5 and ∠9; ∠6 and ∠7
d. ∠7 and ∠12: ∠6 and ∠9

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.

Step2: Analyze each option

• Option A: $\angle4$ and $\angle7$ are vertical angles (not consecutive interior angles). $\angle10$ and $\angle13$ are also vertical angles.
• Option B: $\angle4$ and $\angle16$: There is no transversal - line relationship that makes them consecutive interior angles. $\angle6$ and $\angle10$: When considering the lines \(m\) and \(l\) and the transversal \(k\), \(\angle6\) and \(\angle10\) lie between \(m\) and \(l\) and on the same side of transversal \(k\). But \(\angle4\) and \(\angle16\) do not fit the consecutive - interior - angle definition.
• Option C: $\angle5$ and $\angle9$: When considering the lines \(m\) and \(l\) and the transversal (assuming a non - standard one, but they are actually alternate exterior angles). $\angle6$ and $\angle7$ lie between lines \(m\) and \(n\) and on the same side of transversal \(k\), so they are consecutive interior angles. But \(\angle5\) and \(\angle9\) are not.
• Option D: $\angle7$ and $\angle12$: There is no transversal - line relationship that makes them consecutive interior angles. $\angle6$ and $\angle9$: When considering the lines \(m\) and \(l\) and the transversal \(k\), \(\angle6\) and \(\angle9\) lie between \(m\) and \(l\) and on the same side of transversal \(k\).

Answer:

B. \(\angle4\) and \(\angle16\); \(\angle6\) and \(\angle10\)