Question

19)
20)
-2-

Explanation:

Step1: Use vertical - angle and supplementary - angle relationships

For problem 19:
The angle of \(40^{\circ}\) and the angle adjacent to \(b\) are vertical angles. The sum of adjacent angles on a straight line is \(180^{\circ}\).
Let's assume the angle adjacent to \(b\) is equal to \(40^{\circ}\) (vertical - angle property). Then \(b = 180^{\circ}-40^{\circ}\).

Step2: Calculate the value of \(b\)

\(b=140^{\circ}\)

For problem 20:
\(b\) and \(72^{\circ}\) are vertical angles. By the vertical - angle theorem, vertical angles are equal.
So \(b = 72^{\circ}\)

Answer:

1. \(b = 140^{\circ}\)
2. \(b = 72^{\circ}\)