Question

if m∠1 is 120°, what is the measure of m∠3?
question 2
if m∠8 is 30°, what is the measure of m∠4?

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle2$ are a linear - pair, and $\angle2$ and $\angle3$ are vertical angles. First, find $\angle2$. Since $\angle1$ and $\angle2$ are a linear - pair, $\angle1+\angle2 = 180^{\circ}$. Given $\angle1 = 120^{\circ}$, then $\angle2=180^{\circ}-\angle1$.
$\angle2 = 180 - 120=60^{\circ}$

Step2: Use vertical - angle property

$\angle2$ and $\angle3$ are vertical angles. So, $\angle3=\angle2$.
$\angle3 = 60^{\circ}$

for second question:

Step1: Identify vertical - angle relationship

$\angle8$ and $\angle7$ are a linear - pair, and $\angle7$ and $\angle4$ are vertical angles. First, find $\angle7$. Since $\angle8$ and $\angle7$ are a linear - pair, $\angle8+\angle7 = 180^{\circ}$. Given $\angle8 = 30^{\circ}$, then $\angle7=180^{\circ}-\angle8$.
$\angle7 = 180 - 30=150^{\circ}$

Step2: Use vertical - angle property

$\angle7$ and $\angle4$ are vertical angles. So, $\angle4=\angle7$.
$\angle4 = 150^{\circ}$

Answer:

$60^{\circ}$