Question

which pair of angles are vertical angles?
\\( \angle kre \\) and \\( \angle ert
\\( \angle mrc \\) and \\( \angle krm
\\( \angle ert \\) and \\( \angle mrc
\\( \angle krc \\) and \\( \angle crh \\)

Explanation:

Vertical angles are formed by two intersecting lines and are opposite each other, sharing a common vertex but no common side. Let's analyze each option:

• $\angle KRE$ and $\angle ERT$: These are adjacent angles (share a common side $RE$) and form a linear pair, not vertical angles.
• $\angle MRC$ and $\angle KRM$: These share a common side $RM$ and are adjacent, not vertical angles.
• $\angle ERT$ and $\angle MRC$: These are formed by the intersection of lines $KE$ (or $KC$) and $MT$ (or $MH$). They are opposite each other at vertex $R$, with no common side, so they are vertical angles.
• $\angle KRC$ and $\angle CRH$: These are adjacent angles (share a common side $RC$) and form a linear pair along the horizontal line $KH$, not vertical angles.

Answer:

$\boldsymbol{\angle ERT}$ and $\boldsymbol{\angle MRC}$