Question

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

figure 2
110
64
figure 3

Explanation:

Figure 1

Step1: Find ∠1

Since \(n\parallel m\), ∠1 and the angle equal to \(82^{\circ}\) (vertical - angle to \(82^{\circ}\)) are supplementary.
\(\angle1 = 180^{\circ}-82^{\circ}=98^{\circ}\)

Step2: Find ∠2

∠2 and ∠1 are supplementary (linear - pair).
\(\angle2 = 180^{\circ}-\angle1=180^{\circ}-98^{\circ}=82^{\circ}\)

Figure 2

Step1: Find ∠1

Since \(n\parallel m\), ∠1 and the \(64^{\circ}\) angle are vertical angles.
\(\angle1 = 64^{\circ}\)

Step2: Find ∠2

∠2 and ∠1 are supplementary (linear - pair).
\(\angle2=180^{\circ}-\angle1 = 180^{\circ}-64^{\circ}=116^{\circ}\)

Figure 3

Step1: Find ∠2

∠2 and the \(157^{\circ}\) angle are supplementary (linear - pair).
\(\angle2=180^{\circ}-157^{\circ}=23^{\circ}\)

Step2: Find ∠1

Since \(n\parallel m\), ∠1 and ∠2 are supplementary.
\(\angle1 = 180^{\circ}-\angle2=180^{\circ}-23^{\circ}=157^{\circ}\)

Answer:

Figure	∠1	∠2
2	\(64\)	\(116\)
3	\(157\)	\(23\)