Question

angle pair relationships
name the relationship: complementary, linear - pair, vertical, or adjacent.
1)
2)
3)
4)
5)
6)
7)
8)
find the measure of angle b.
9)
10)
11)
12)

Explanation:

Step1: Recall angle - pair relationships

Complementary angles sum to 90°, linear - pair angles sum to 180°, vertical angles are equal, and adjacent angles share a common side and vertex.

Step2: Analyze each pair for relationships

For the angle - measure problems:

Problem 9

The two angles are a linear pair.
Let the measure of angle \(b\) and 50° be a linear pair.
Since the sum of angles in a linear pair is 180°, we have \(b + 50^{\circ}=180^{\circ}\).
Solve for \(b\): \(b=180^{\circ}-50^{\circ}=130^{\circ}\).

Problem 10

The two angles are vertical angles.
Since vertical angles are equal, if one angle is 45°, then \(b = 45^{\circ}\).

Problem 11

The sum of the angles around a point is 360°.
We know two of the angles are 209° and 96°. Let \(b\) be the third angle.
So, \(b+209^{\circ}+96^{\circ}=360^{\circ}\).
First, add the known angles: \(209^{\circ}+96^{\circ}=305^{\circ}\).
Then, solve for \(b\): \(b = 360^{\circ}-305^{\circ}=55^{\circ}\).

Problem 12

The two angles are a linear pair.
Since the sum of angles in a linear pair is 180°, and one angle is 63°, then \(b=180^{\circ}-63^{\circ}=117^{\circ}\).

Answer:

1. \(130^{\circ}\)
2. \(45^{\circ}\)
3. \(55^{\circ}\)
4. \(117^{\circ}\)