To solve for the angle measures, we can use the properties of parallel lines and triangles:

1. m∠1: Since ∠1 and the angle marked 52° are alternate interior angles (because of the parallel lines), they are congruent.

   • m∠1 = 52°

2. m∠2: This angle is supplementary to ∠1 because they are on the same straight line.

   • m∠2 = 180° - 52° = 128°

3. m∠3: Since angles in a triangle add up to 180°, we can find m∠3 by adding the given 47° and m∠5 (which is vertically opposite to ∠3, hence m∠5 = m∠3).

4. m∠4: Angle 4 is on a straight line with angle 3, making it supplementary.

Would you like the solution for each step expanded with more details?

Here are five questions that might interest you:

1. How do parallel line properties help in finding unknown angles?
2. What is the sum of angles in any triangle, and how does it help solve problems like this?
3. How can alternate interior angles be identified?
4. What is the significance of supplementary angles on a straight line?
5. Can angles vertically opposite each other in intersecting lines be proven equal?

Tip: Always look for congruent angles when working with parallel lines!