Question

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: Identify the relationship in 1)

Check if angles \(a\) and \(b\) share a common side and vertex.
They are adjacent.

Step2: Identify the relationship in 2)

Check if angles \(a\) and \(b\) are adjacent.
They are adjacent.

Step3: Identify the relationship in 3)

Check if angles \(a\) and \(b\) are adjacent.
They are adjacent.

Step4: Identify the relationship in 4)

Check if \(a + b=90^{\circ}\).
They are complementary.

Step5: Identify the relationship in 5)

Check if angles \(a\) and \(b\) are opposite each other.
They are vertical.

Step6: Identify the relationship in 6)

Check if angles \(a\) and \(b\) are adjacent.
They are adjacent.

Step7: Identify the relationship in 7)

Check if \(a + b = 180^{\circ}\).
They are a linear pair.

Step8: Identify the relationship in 8)

Check if angles \(a\) and \(b\) are adjacent.
They are adjacent.

Step9: Find measure of \(b\) in 9)

Use the property of vertical angles.
\(b = 50^{\circ}\)

Step10: Find measure of \(b\) in 10)

Use the property of vertical angles.
\(b = 43^{\circ}\)

Step11: Find measure of \(b\) in 11)

Use the fact that the sum of angles around a point is \(360^{\circ}\).
\(b=360^{\circ}-209^{\circ}-96^{\circ}=55^{\circ}\)

Step12: Find measure of \(b\) in 12)

Use the fact that the sum of angles in a right - angled configuration (\(90^{\circ}\)) is considered.
\(b = 90^{\circ}-63^{\circ}=27^{\circ}\)

Answer:

1. Adjacent
2. Adjacent
3. Adjacent
4. Complementary
5. Vertical
6. Adjacent
7. Linear pair
8. Adjacent
9. \(50^{\circ}\)
10. \(43^{\circ}\)
11. \(55^{\circ}\)
12. \(27^{\circ}\)