Question

Question number 1 and 2 and find measure of. angle 1

Answer 1

`\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}`

Step-by-step explanation

Step 1

vertical angles:

Vertical angles are pair angles formed when two lines intersect

`m\measuredangle x=m\measuredangle y`

so, we need to find a vertical angle in

a)

Figure 1:

blue angles are vertical, so

`m\measuredangle HML\text{ and m}\measuredangle JMK`

Figure 2:

hence, a pair of vertical angle is

`\begin{gathered} \\ m\measuredangle LQM\text{ and m}\measuredangle\text{PQN} \end{gathered}`

Step 2

pair of adjacent angles:

Adjacent angles are two angles that have a common vertex and a common side but do not overlap

`m\measuredangle x\text{ is adjacent to m}\measuredangle y`

then

a)

for Figure 1

pair of adjacent angles

`m\measuredangle HMJ\text{ and m}\measuredangle JMK`

b) for Figure 2

pair of adjacent angles

`m\measuredangle LQM\text{ and m}\measuredangle LQR`

I hope this helps you