Question

consider the figures shown below. find the values of ∠1 and ∠2 for the given figures and complete the table accordingly. note: enter numeric values only. figures angle 1 angle 2 figure 1 figure 2 figure 3

Explanation:

Step1: Identify angle - pair relationship in Figure 1

In Figure 1, $\angle1$ and the $82^{\circ}$ angle are corresponding angles (assuming $m\parallel n$). So $\angle1 = 82^{\circ}$. $\angle1$ and $\angle2$ are supplementary (a linear - pair), so $\angle2=180 - 82=98^{\circ}$.

Step2: Identify angle - pair relationship in Figure 2

In Figure 2, $\angle1$ and the $64^{\circ}$ angle are vertical angles. So $\angle1 = 64^{\circ}$.

Step3: Identify angle - pair relationship in Figure 3

In Figure 3, $\angle2$ and the $157^{\circ}$ angle are vertical angles. So $\angle2 = 157^{\circ}$. $\angle1$ and $\angle2$ are supplementary (assuming $m\parallel n$), so $\angle1=180 - 157 = 23^{\circ}$.

Answer:

Figures	Angle 1	Angle 2
Figure 2	64	64
Figure 3	23	157