Question

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

Explanation:

1)

Step1: Use the property of alternate interior angles

When two parallel lines are cut by a transversal, alternate interior angles are equal.
So, \(x = 68^{\circ}\)

2)

Step1: Use the property of vertical angles

Vertical angles are equal.
So, \(x = 114^{\circ}\)

3)

Step1: Use the property of corresponding angles

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

4)

Step1: Use the property of supplementary angles

\(120^{\circ}+x = 180^{\circ}\) (co - interior angles for parallel lines cut by a transversal)
\(x=180^{\circ}- 120^{\circ}\)
\(x = 60^{\circ}\)

5)

Step1: Use the property of vertical angles

Vertical angles are equal.
So, \(x = 55^{\circ}\)

6)

Step1: Use the property of corresponding angles

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

7)

Step1: Use the property of supplementary angles

\(x + 149^{\circ}=180^{\circ}\) (linear pair)
\(x=180^{\circ}-149^{\circ}\)
\(x = 31^{\circ}\)

8)

Step1: Use the property of vertical angles

Vertical angles are equal.
So, \(x = 40^{\circ}\)

Answer:

1. \(x = 68^{\circ}\)
2. \(x = 114^{\circ}\)
3. \(x = 74^{\circ}\)
4. \(x = 60^{\circ}\)
5. \(x = 55^{\circ}\)
6. \(x = 71^{\circ}\)
7. \(x = 31^{\circ}\)
8. \(x = 40^{\circ}\)