Let's work through the questions in the image one by one:

Q83: In Fig. 5.43, write all the pairs of supplementary angles.

• Supplementary angles are two angles whose measures add up to 180°. In Fig. 5.43:
  • ∠5 + ∠6
  • ∠3 + ∠4
  • ∠7 + ∠8
  • ∠2 + ∠1

These are the supplementary angle pairs because they are on a straight line, and their measures sum up to 180°.

Q84: What is the type of other angle of a linear pair if:

• (a) One of its angles is acute?

  • The other angle must be obtuse because an acute angle is less than 90°, and the other must be larger than 90° to sum up to 180°.

• (b) One of its angles is obtuse?

  • The other angle must be acute, as an obtuse angle is more than 90°, and the other angle must be less than 90° to make the total 180°.

• (c) One of its angles is right?

  • The other angle must also be right because a right angle is 90°, and the pair must sum to 180°, meaning both angles are 90°.

Q85: Can two acute angles form a pair of supplementary angles? Give a reason in support of your answer.

• No, two acute angles cannot form a pair of supplementary angles because acute angles are both less than 90°, and their sum would be less than 180°, which is required for supplementary angles.

Q86: Two lines AB and CD intersect at O (Fig. 5.44). Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only.

• Adjacent angles share a common arm.
  • ∠1 and ∠2
  • ∠2 and ∠3
  • ∠3 and ∠4
  • ∠4 and ∠1

These are the pairs of adjacent angles.

Q87: If the complement of an angle is 62°, then find its supplement.

• The complement of an angle is what adds to 90°. So the original angle is: $\text{Original angle} = 90° - 62° = 28°$
  • Now, its supplement is what adds to 180°, so: $\text{Supplement} = 180° - 28° = 152°$

The supplement of the angle is 152°.

Q88: A road crosses a railway line at an angle of 30° as shown in Fig. 5.45. Find the values of a, b, and c.

• In this diagram:
  • a and 30° are alternate interior angles, so: $a = 30°$
  • b and c are supplementary since they form a straight line: $b = 180° - 30° = 150°$
  • c and a are also equal due to corresponding angles: $c = 30°$

So, $a = 30°$, $b = 150°$, and $c = 30°$.

Would you like any more details or have any questions about these solutions? Here are 5 follow-up questions that expand on this:

1. How do we calculate supplementary angles for different types of intersecting lines?
2. What is the relationship between adjacent angles and supplementary angles?
3. Why can two acute angles never be supplementary?
4. How can we apply the concept of linear pairs in real-world situations?
5. Can two obtuse angles form a pair of supplementary angles? Why or why not?

Tip: Always check the sum of angles in geometry to determine relationships such as supplementary, complementary, or vertical angles!