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Let's go through each of the sub-questions one by one:

**(i)** The number of angles formed by a transversal of two lines:
- A transversal intersecting two lines creates different types of angles (corresponding, alternate interior, alternate exterior, etc.). For two lines, a transversal forms **8 angles**.
- **Answer: (C) 8**

**(ii)** How many midpoints does a segment have?
- A line segment has exactly **one midpoint**.
- **Answer: (A) only one**

**(iii)** A transversal intersects two parallel lines. If the measure of one of the angles is 40°, then the measure of its corresponding angle is:
- Corresponding angles formed by a transversal with parallel lines are equal.
- So, if one angle is 40°, its corresponding angle is also 40°.
- **Answer: (A) 40°**

**(iv)** In △PQR, if ∠R > ∠Q, then...
- In any triangle, the side opposite the larger angle is longer. If ∠R > ∠Q, then the side opposite ∠R (which is side PQ) is longer than the side opposite ∠Q (which is side PR).
- **Answer: (B) PQ > PR**

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Do you need any further clarification on these answers?

Here are 5 related questions to further explore this topic:
1. How many angles are formed when a transversal intersects three lines?
2. Can a line segment have more than one midpoint in non-Euclidean geometry?
3. How do alternate interior angles compare when a transversal intersects two parallel lines?
4. What is the sum of all interior angles in a triangle?
5. How can we prove that corresponding angles are congruent using properties of parallel lines?

**Tip:** When dealing with triangles, remember that the longest side is always opposite the largest angle!

Q.1. (A) Four alternative answers are given for each of the following sub-questions. Choose the correct alternative and write the alphabet of that answer:
(i) The number of angles formed by a transversal of two lines is?
(ii) How many midpoints does a segment have?
(iii) A transversal intersects two parallel lines. If the measure of one of the angles is 40°, then the measure of its corresponding angle is?
(iv) In △PQR, if ∠R > ∠Q, then?

This geometry problem covers key concepts such as angles formed by transversals, properties of line segments, and the relationship between angles in triangles. The questions involve transversals intersecting parallel lines, midpoints, and angle comparisons in triangles. Ideal for students in Grades 8-10.

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