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°.