Question

find the measure of angle b.
21)
22)
23)
24)
25)
26)

Explanation:

Step1: Vertical Angles

Vertical angles are equal. In problem 21, angle \(b\) and \(57^{\circ}\) are vertical angles. So \(b = 57^{\circ}\).

Step2: Linear Pair

In problem 22, \(53^{\circ}\) and \(b\) form a linear pair (\(a + b=180^{\circ}\) for a linear pair). So \(b=180 - 53=127^{\circ}\).

Step3: Linear Pair

In problem 23, \(113^{\circ}\) and \(b\) form a linear pair. So \(b = 180-113 = 67^{\circ}\).

Step4: Vertical Angles

In problem 24, angle \(b\) and \(40^{\circ}\) are vertical angles. So \(b = 40^{\circ}\).

Step5: Vertical Angles

In problem 25, \(b\) and \(95^{\circ}\) are vertical angles. But wait, no! Wait, if two lines are crossed by a transversal and we consider the relationship. Wait, actually, if we assume the two horizontal - like lines are parallel (by the arrow marks), and using the property of corresponding angles or vertical angles. Wait, no, actually, \(b\) and \(95^{\circ}\) are supplementary (if we consider the straight - line property). Wait, no, if we consider the vertical - angle and linear - pair relationships. Wait, actually, \(b\) and \(95^{\circ}\) are vertical angles? No. Wait, if we consider the two intersecting lines, \(b\) and \(95^{\circ}\) are adjacent angles forming a linear pair. Wait, no, if we assume the two parallel lines (marked with arrows) and a transversal. Wait, no, the two angles \(b\) and \(95^{\circ}\) are vertical angles. Wait, no, if we have two intersecting lines, \(b\) and \(95^{\circ}\) are adjacent and form a linear pair. Wait, no, actually, if we consider the two lines, \(b + 95=180\) (linear pair), so \(b = 85^{\circ}\).

Step6: Vertical Angles

In problem 26, \(b\) and \(35^{\circ}\) are vertical angles. So \(b = 35^{\circ}\).

Answer:

1. \(57^{\circ}\)
2. \(127^{\circ}\)
3. \(67^{\circ}\)
4. \(40^{\circ}\)
5. \(85^{\circ}\)
6. \(35^{\circ}\)