Question

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

Explanation:

1)

Step1: Use the property of corresponding angles

Corresponding angles are equal. So \(x = 45^{\circ}\)

2)

Step1: Use the property of vertical angles

Vertical angles are equal. So \(x=102^{\circ}\)

3)

Step1: Use the property of alternate - interior angles

Alternate - interior angles are equal. So \(x = 119^{\circ}\)

4)

Step1: Use the property of corresponding angles

Corresponding angles are equal. So \(x = 53^{\circ}\)

5)

Step1: Use the property of same - side interior angles

Same - side interior angles are supplementary (\(x + 136^{\circ}=180^{\circ}\))

Step2: Solve for \(x\)

\(x=180^{\circ}-136^{\circ}=44^{\circ}\)

6)

Step1: Use the property of vertical angles

Vertical angles are equal. So \(x = 97^{\circ}\)

7)

Step1: Use the property of vertical angles

Vertical angles are equal. So \(x = 34^{\circ}\)

8)

Step1: First, find the angle adjacent to \(142^{\circ}\)

The adjacent angle to \(142^{\circ}\) is \(180^{\circ}-142^{\circ}=38^{\circ}\) (supplementary angles)

Step2: Then, use the property of vertical angles

\(x\) and the angle found in Step1 are vertical angles. So \(x = 38^{\circ}\)

Answer:

1. \(x = 45^{\circ}\)
2. \(x = 102^{\circ}\)
3. \(x = 119^{\circ}\)
4. \(x = 53^{\circ}\)
5. \(x = 44^{\circ}\)
6. \(x = 97^{\circ}\)
7. \(x = 34^{\circ}\)
8. \(x = 38^{\circ}\)