To solve the questions 8 and 9 from the image, let's analyze the content and geometry.

Question 8:

It states:

"In the figure, DE ∥ BC, ∠B = 30°, ∠A = 50°. Find the angles."

Solution:

1. Understand the Setup:

   • DE is parallel to BC.
   • ∠B = 30°, ∠A = 50°.
   • Since DE is parallel to BC, this is a trapezium or a triangle with parallel sides.

2. Using Angle-Sum Property of a Triangle: In triangle ABC:

   • The sum of angles in any triangle is $180^\circ$: $\text{∠A} + \text{∠B} + \text{∠C} = 180^\circ$ Substituting: $50^\circ + 30^\circ + \text{∠C} = 180^\circ$ Solving for ∠C: $\text{∠C} = 180^\circ - 50^\circ - 30^\circ = 100^\circ$

3. Conclusion:

   • ∠A = 50°,
   • ∠B = 30°,
   • ∠C = 100°.

Question 9:

It states:

"In the figure, find ∠1 + ∠2 + ∠3 + ∠4 + ∠5."

Solution:

1. Understanding the Polygon: The figure shown is a pentagon with interior angles marked as ∠1, ∠2, ∠3, ∠4, and ∠5.

2. Sum of Interior Angles of a Pentagon: The sum of the interior angles of an $n$-sided polygon is given by: $\text{Sum of interior angles} = (n - 2) \cdot 180^\circ$ For a pentagon ($n = 5$): $\text{Sum of interior angles} = (5 - 2) \cdot 180^\circ = 3 \cdot 180^\circ = 540^\circ$

3. Conclusion: The sum of ∠1 + ∠2 + ∠3 + ∠4 + ∠5 is: $\boxed{540^\circ}$

Final Answers:

• Question 8: ∠A = 50°, ∠B = 30°, ∠C = 100°.
• Question 9: ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 540°.

Would you like step-by-step diagrams or further clarifications?

Here are 5 follow-up questions to explore:

1. What is the sum of exterior angles of any polygon?
2. How do parallel lines affect angle calculations in polygons?
3. What are the properties of trapeziums regarding angle relationships?
4. Can a pentagon have equal angles? If yes, what would they measure?
5. How would the angle sum change for a hexagon or heptagon?

Tip: Always check for parallel lines and symmetry in figures—they simplify angle relationships!