Subjects geometry

Consecutive Interior Angles

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Consecutive Interior Angles


1. **State the problem:** Identify which pairs of angles are consecutive interior angles given the lines and transversal with labeled points. 2. **Recall the definition:** Consecutive interior angles are pairs of angles that lie between two lines on the same side of the transversal. 3. **Analyze each angle pair:** - ∠RQN and ∠ONQ: ∠RQN is at point Q and ∠ONQ at point N. Points R and O lie on opposite sides of the transversal, so these angles are on opposite sides, hence not consecutive interior. - ∠RQN and ∠ONL: ∠RQN at Q, ∠ONL at N but with point L on the opposite side to R. These are not on the same side between the lines so not consecutive interior. - ∠RQN and ∠MNQ: ∠RQN at Q and ∠MNQ at N. Points M and R lie on the same side of the transversal and both angles lie between the two lines, so these are consecutive interior angles. - ∠RQN and ∠PQN: Both angles are at point Q, which is on the transversal. Since they share the point, they cannot be consecutive interior angles between two distinct lines. **Final answer:** The consecutive interior angles are **∠RQN and ∠MNQ**.