Question

angle relationships & measurements (basic)
name the relationship: supplementary, vertical, adjacent, or corresponding.
1)
2)
3)
4)
5)
6)
7)
8)
find the measure of angle b.
9)
10)
-1-

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are opposite angles formed by the intersection of two lines. They are equal in measure.

Step2: Analyze each pair of angles

1. In the first figure, angles \(a\) and \(b\) are formed by the intersection of two lines and are opposite each other. So, they are vertical angles.
2. In the second figure, angles \(a\) and \(b\) are vertical angles.
3. In the third figure, angles \(a\) and \(b\) are vertical angles.
4. In the fourth figure, angles \(a\) and \(b\) are vertical angles.
5. In the fifth figure, angles \(a\) and \(b\) are adjacent angles (they share a common side and a common vertex).
6. In the sixth figure, angles \(a\) and \(b\) are corresponding angles (they are in the same relative position with respect to the parallel lines and the transversal).
7. In the seventh figure, angles \(a\) and \(b\) are adjacent angles.
8. In the eighth figure, angles \(a\) and \(b\) are corresponding angles.

For finding the measure of angle \(b\) in the ninth figure:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to \(180^{\circ}\).

Step2: Calculate the measure of angle \(b\)

If one angle is \(76^{\circ}\), then \(b = 180^{\circ}-76^{\circ}=104^{\circ}\)

For the tenth figure, there seems to be an error in the given answer \(b = 310^{\circ}\) as the sum of angles around a point is \(360^{\circ}\). Let \(b\) be the unknown angle. Then \(b+30^{\circ}+299^{\circ}=360^{\circ}\).

Step1: Set up the equation

\(b+30 + 299=360\)

Step2: Solve for \(b\)

\(b=360-(30 + 299)=360 - 329=31^{\circ}\)

Answer:

1. Vertical
2. Vertical
3. Vertical
4. Vertical
5. Adjacent
6. Corresponding
7. Adjacent
8. Corresponding
9. \(104^{\circ}\)
10. \(31^{\circ}\)