Question

$$ \overleftrightarrow { l n } $$ and $$ \overleftrightarrow { o q } $$ are parallel lines. which angles are vertical angles? $$ \angle q p m $$ and $$ \angle q p r $$ $$ \angle q p m $$ and $$ \angle l m p $$ $$ \angle q p m $$ and $$ \angle l m k $$ $$ \angle q p m $$ and $$ \angle o p r $$

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other.

Step2: Analyze each option

• For $\angle QPM$ and $\angle QPR$: These are adjacent angles (share a common side $QP$), so they are not vertical angles.
• For $\angle QPM$ and $\angle LMP$: These are not formed by the intersection of the same two lines. $\angle QPM$ is formed by lines $OQ$ and $KR$, and $\angle LMP$ is formed by lines $LN$ and $KR$.
• For $\angle QPM$ and $\angle LMK$: $\angle QPM$ is formed by lines $OQ$ and $KR$, and $\angle LMK$ is formed by lines $LN$ and $KR$. They are not vertical angles.
• For $\angle QPM$ and $\angle OPR$: Lines $OQ$ and $KR$ intersect at point $P$. $\angle QPM$ and $\angle OPR$ are non - adjacent and opposite each other at the intersection of lines $OQ$ and $KR$.

Answer:

$\angle QPM$ and $\angle OPR$