From the image, you have a set of intersecting lines, with various angles labeled. Let's break down the angles to determine the missing angle $b$:

1. Vertical Angles: We notice that the two lines form pairs of vertical (opposite) angles, which are congruent. This means the angles that lie directly across from each other are equal.

2. Adjacent Angles on a Straight Line: The sum of two adjacent angles along a straight line is 180°.

Steps to Solve:

• The angle adjacent to 74° is the unknown angle $b$. Since they are on a straight line, we can use the property of supplementary angles: $74° + b = 180°$ $b = 180° - 74° = 106°$

Thus, $b = 106^\circ$.

Let me know if you'd like further details or explanations!

Follow-up Questions:

1. What is the name of the property used to find $b$ in relation to 74°?
2. Can you explain how vertical angles work in intersecting lines?
3. How would you find the unknown angle across from 67°?
4. What is the sum of the angles around any point where lines intersect?
5. How do you use complementary and supplementary angles to solve problems like this?

Tip:

Always remember: adjacent angles on a straight line add up to 180°, while vertical angles are always equal.