[tex]\begin{gathered} 1)\text{ vertical} \\ m\measuredangle HML\text{ and m}\measuredangle JMK\text{ , } \\ m\measuredangle LQM\text{ and m}\measuredangle\text{PQN} \\ 2)\text{ adjacents} \\ m\measuredangle HMJ\text{ and m}\measuredangle JMK \\ m\measuredangle LQM\text{ and m}\measuredangle LQR \end{gathered}[/tex]
Explanation
Step 1
vertical angles:
Vertical angles are pair angles formed when two lines intersect
[tex]m\measuredangle x=m\measuredangle y[/tex]
so, we need to find a vertical angle in
a)
Figure 1:
blue angles are vertical, so
[tex]m\measuredangle HML\text{ and m}\measuredangle JMK[/tex]
Figure 2:
hence, a pair of vertical angle is
[tex]\begin{gathered} \\ m\measuredangle LQM\text{ and m}\measuredangle\text{PQN} \end{gathered}[/tex]
Step 2
pair of adjacent angles:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap
[tex]m\measuredangle x\text{ is adjacent to m}\measuredangle y[/tex]
then
a)
for Figure 1
pair of adjacent angles
[tex]m\measuredangle HMJ\text{ and m}\measuredangle JMK[/tex]
b) for Figure 2
pair of adjacent angles
[tex]m\measuredangle LQM\text{ and m}\measuredangle LQR[/tex]
I hope this helps you
