Question

#7: ∠qpn and ____ are vertical angles. *
∠rpq
∠mpn
∠mpo
∠rpo
#8: ∠mpo and ____ are adjacent & congruent angles. *
∠mpq
∠opr
∠mpn
∠rpq

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other.

Step2: Analyze for ∠QPN

When considering ∠QPN, the vertical - angle pair is formed by the intersection of the relevant lines. ∠QPN and ∠MPO are vertical angles.

Step3: Recall adjacent - and - congruent - angle definition

Adjacent angles share a common side and a common vertex. Congruent angles have the same measure.

Step4: Analyze for ∠MPO

∠MPO and ∠OPR are adjacent (share side $\overrightarrow{OP}$) and if they are congruent (equal measure), they satisfy the condition.

Answer:

#7: ∠MPO
#8: ∠OPR