The image shows a geometry problem involving parallel lines and angles. The diagram indicates a pair of parallel lines crossed by a transversal, creating several angles. Specifically, you are asked to find the measure of angle 3.

Here’s how we can solve it:

• Angles 3 and 1 form a linear pair (on a straight line), meaning they are supplementary (sum to 180°).
• Angle 1 and the given angle (40°) are corresponding angles because they are on the same side of the transversal and in the same relative position. Therefore, angle 1 is also 40°.

Now, knowing that angles 3 and 1 are supplementary: $\text{Angle 3} = 180° - 40° = 140°$

Thus, the measure of angle 3 is 140°.

Would you like more details, or do you have any further questions?

Here are 5 related questions for deeper understanding:

1. How can we identify corresponding angles in parallel line diagrams?
2. What is the difference between alternate interior and corresponding angles?
3. How do we prove that corresponding angles are equal when two lines are parallel?
4. Can two non-parallel lines have corresponding angles equal?
5. What other angle pairs exist in parallel line and transversal problems?

Tip: When working with parallel lines and a transversal, always look for angle relationships like corresponding, alternate interior, and linear pairs to simplify calculations.