Question

which angles are consecutive interior angles?
diagram with lines ln, oq and transversal kr intersecting at m and p respectively
options:
∠nmp and ∠opr
∠qpm and ∠nmp
∠qpm and ∠lmk
∠lmk and ∠nmk

Explanation:

Step1: Recall consecutive interior angles definition

Consecutive interior angles are on the same side of a transversal, between two parallel lines.

Step2: Analyze the diagram

Lines LN and OQ are parallel (both horizontal), transversal KR intersects them at M and P. Check angle pairs:

• ∠NMP (at M, right of KR, between LN & OQ) and ∠OPR (at P, left of KR, between LN & OQ) are on opposite sides of KR → no.
• ∠QPM (at P, right of KR, between LN & OQ) and ∠NMP (at M, right of KR, between LN & OQ) are same side of transversal, between parallel lines → yes.
• ∠QPM and ∠LMK (∠LMK is above LN) → not between parallel lines → no.
• ∠LMK and ∠NMK (linear pair, not between parallel lines) → no.

Answer:

∠QPM and ∠NMP