Question

find the value of each indicated angle.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: For problem 3

When two lines are parallel and cut by a transversal, corresponding angles are equal. Here, \(x\) and \(74^{\circ}\) are corresponding angles.
\(x = 74^{\circ}\)

Step2: For problem 4

When two lines are parallel and cut by a transversal, consecutive - interior angles are supplementary. The angle of \(120^{\circ}\) and \(x\) are consecutive - interior angles.
\(x=180^{\circ}- 120^{\circ}\)
\(x = 60^{\circ}\)

Step3: For problem 5

When two lines intersect, vertical angles are equal. The angle of \(55^{\circ}\) and \(x\) are vertical angles.
\(x = 55^{\circ}\)

Step4: For problem 6

When two lines are parallel and cut by a transversal, corresponding angles are equal. Here, \(x\) and \(71^{\circ}\) are corresponding angles.
\(x = 71^{\circ}\)

Step5: For problem 7

When two lines intersect, vertical angles are equal. The angle of \(149^{\circ}\) and its adjacent angle form a linear pair. The adjacent angle of \(149^{\circ}\) is \(180 - 149=31^{\circ}\). And \(x\) and the \(31^{\circ}\) angle are vertical angles.
\(x = 31^{\circ}\)

Answer:

1. \(60^{\circ}\)
2. \(60^{\circ}\)
3. \(55^{\circ}\)
4. \(71^{\circ}\)
5. \(31^{\circ}\)