https://file.aiquickdraw.com/mathbot/file/1726581867087el8ny5z0.jpg

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.

Determine the missing angle b given that the adjacent angle is 74° and the lines are intersecting with other angles provided (67°, 113°).

Learn how to determine the missing angle b in a set of intersecting lines using the concept of supplementary angles. This problem involves working with adjacent angles, vertical angles, and applying the angle sum property. Suitable for students in Grades 6-8.

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