Video: Identifying Consecutive Interior Angles

Which of the following angle pairs are consecutive interior angles? [A] βˆ π‘ and βˆ π‘˜ [B] βˆ π‘ and βˆ π‘— [C] βˆ π‘‘ and βˆ π‘“ [D] βˆ π‘‘ and βˆ π‘– [E] βˆ π‘“ and βˆ π‘˜.

02:43

Video Transcript

Which of the following angle pairs are consecutive interior angles? A) angle 𝑏 and angle π‘˜, B) angle 𝑐 and angle 𝑗, C) angle 𝑑 and angle 𝑓, D) angle 𝑑 and angle 𝑖, or E) angle 𝑓 and angle π‘˜.

First, we need to consider the definition of consecutive interior angles. They are the pair of angles on one side of the transversal but inside the two lines. If we have two lines and a transversal, here are two consecutive angles. They fall on the same side of the transversal and inside the two lines. So, let’s consider our five options. A says angle 𝑏 and angle π‘˜. In this case, the line highlighted in blue is the transversal, and 𝑏 and π‘˜ are on opposite sides of the transversal, which means they’re not consecutive interior angles.

Option B is angle 𝑐 and angle 𝑗. And again, these angles are on opposite sides of the transversal, which means they’re not consecutive interior angles. Next up, we have angle 𝑑 and angle 𝑓. Angle 𝑑 and angle 𝑓 have a different transversal. This time, the two angles are on one side of the transversal. They’re both above the transversal. But the consecutive interior angles would be angle 𝑑 and angle 𝑒 because they need to be inside the two lines. So, we can eliminate option C. Next, we have option D, which is angle 𝑑 and angle 𝑖. These two angles are not on the same side of their transversal.

So, let’s check angle 𝑓 and angle π‘˜. If we look at these angles, this is their transversal. They’re both on the same side of their transversal. And they are inside the two lines, which makes angle 𝑓 and angle π‘˜ consecutive interior angles. It’s important to note here that there are many different pairs of consecutive interior angles in this figure. For example, if we let this be the transversal, 𝑐 and β„Ž are consecutive interior angles and so are 𝑑 and 𝑒. We’ve chosen 𝑓 and π‘˜ out of the given list, but as long as the pair of angles are on the same side of the transversal and inside the two lines, they are consecutive interior angles.

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