https://file.aiquickdraw.com/mathbot/file/1725581187675fg49lx7p.jpg

The problem asks to find the **measure of the missing angles** shown in the image. The diagram is a set of intersecting lines that forms several angles around a point.

The angle provided is labeled **140°**, and the task is to find the missing angles. Since the sum of angles around a point is always **360°**, we can calculate the other angles.

### Step-by-Step Solution:

1. There are four angles formed around the point where the lines intersect.
2. One of the angles is given as **140°**.
3. Let’s denote the unknown angles as **x** (the vertical opposite of the 140° angle) and **y** (the remaining two angles).

### Vertical Opposite Angle:
- The angle opposite to **140°** is also **140°**, due to the property of vertical angles being equal.

### Remaining Angles:
- The two remaining angles form a straight line with the 140° angles. A straight line has a total of **180°**.
- Therefore, the sum of the two unknown angles must be:
  \[
  180° - 140° = 40°
  \]
  Since the two angles are equal (as they are vertical angles), each of them is:
  \[
  \frac{40°}{2} = 20°
  \]

### Conclusion:
- The unknown angles are **140°** and **20°**.

Would you like more details on this, or have any questions? 

Here are five related questions you could explore:
1. What is the sum of angles at a point?
2. How do vertical angles relate to each other?
3. What is the definition of supplementary angles?
4. How do you calculate angles when lines are intersected by a transversal?
5. Can two adjacent angles be unequal but still form a linear pair?

**Tip:** Always remember that vertical angles are congruent, and the sum of angles on a straight line is 180°.

Learn how to find missing angles in a set of intersecting lines using the vertical angle theorem and the linear pair theorem. This problem explains how to calculate unknown angles, with one angle given as 140°. Suitable for students in Grades 6-8.

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