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

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!