Welcome to AssamSchool. This article contains 30 Extra Questions from Lines and Angles from Class 9 Mathematics Chapter 6. These Lines and Angles Class 9 Extra Questions are helpful to test your understanding and knowledge of the chapter. These additional questions will not only help you to excel in the chapter but also will give you a strong foundation in Mathematics.
We have also provided step-by-step answers to the questions for reference. So, let’s start…
30 Lines and Angles Class 9 Extra Questions
1. Define “linear pair of angles” with an example.
2. What are vertically opposite angles? Illustrate with a diagram.
3. If two angles are supplementary and one is \(60°\), find the other.
4. True or False: Adjacent angles always form a linear pair. Justify.
5. Name the type of angle formed when the time is 3:00 on a clock.
6. If \(∠A\) and \(∠B\) are complementary, and \(∠A = 35°\), find \(∠B\).
7. State the Linear Pair Axiom.
8. Identify the arms and vertex of \(∠XYZ\).
9. If two lines intersect, how many pairs of vertically opposite angles are formed?
10. What is the measure of a reflex angle if its corresponding acute angle is \(45°\)?
11. In Fig. 6.8 (intersecting lines), if \(∠AOC = 70°\), find \(∠BOD\) and \(∠AOD\).
12. Prove that the bisectors of a linear pair form a right angle.
13. If a transversal intersects two parallel lines, state the relationship between alternate interior angles.
14. In Fig. 6.10, if \(∠POS = 80°\), find \(∠ROT\).
15. Two lines intersect to form four angles. If one angle is \(110°\), find all other angles.
16. If \(∠1\) and \(∠2\) are vertically opposite angles, and \(∠1 = 3x + 10°\), \(∠2 = 5x − 30°\), solve for \(x\).
17. In Fig. 6.19, if \(PQ || RS\) and \(∠MXQ = 120°\), find \(∠XMY\).
18. If the ratio of two supplementary angles is \(2:3\), find the angles.
19. Prove that the sum of all angles around a point is \(360°\).
20. In Fig. 6.26, if \(∠APQ = 50°\), find \(∠PRD\).
21. Prove that if two lines are parallel to a third line, they are parallel to each other.
22. In Fig. 6.20, if \(AB || PQ || RS\) and \(∠BMY = 50°\), find \(∠XMB\).
23. If the bisectors of a pair of alternate interior angles are parallel, prove the lines are parallel.
24. In Fig. 6.22, if \(AB || CD || EF\) and \(∠BEF = 60°\), find \(x, y, z\).
25. Prove that the vertically opposite angles formed by intersecting lines are equal.
26. In Fig. 6.27, if mirrors \(PQ\) and \(RS\) are parallel, prove \(AB || CD\) using reflection laws.
27. If two adjacent angles are equal and form a linear pair, prove each is \(90°\).
28. In Fig. 6.25, if \(PQ || ST\) and \(∠QRS = 100°\), find \(∠PQR\) and \(∠RST\).
29. If a transversal intersects two lines such that corresponding angles are equal, prove the lines are parallel.
30. In Fig. 6.24, if \(EF ⊥ CD\) and \(∠GED = 130°\), find \(∠AGE\) and \(∠FGE\).
Answers
- Answer:
A linear pair consists of two adjacent angles whose non-common arms are opposite rays. Example: \(∠ABD\) and \(∠DBC\) in Fig. 6.3 in textbook. - Answer:
Vertically opposite angles are formed when two lines intersect. They are equal. Example: \(∠AOD\) and \(∠BOC\) in Fig. 6.4. - Answer:
Supplementary angles sum to \(180°\). If one is \(60°\), the other is \(120°\). - Answer:
False. Adjacent angles share a common arm and vertex but need not sum to \(180°\). - Answer:
Right angle \(90°\). - Answer:
\(∠B = 90° − 35° = 55°\) - Answer:
If a ray stands on a line, the sum of the two adjacent angles is \(180°\). - Answer:
Arms: \(YX\) and \(YZ\); Vertex: \(Y\). - Answer:
Two pairs. - Answer:
Reflex angle = \(360° − 45°\) = \(315°\). - Answer:
\(∠BOD = 70°\) (vertically opposite to \(∠AOC\)). \(∠AOD = 180° − 70° = 110°\). - Answer:
Let \(∠AOC\) and \(∠BOC\) form a linear pair. Their bisectors create angles summing to \(90°\), forming a right angle. - Answer:
Alternate interior angles are equal. - Answer:
\(∠ROT = 90°\) (as proved in Example 2). - Answer:
Angles: \(110°, 70°, 70°, 110°\) - Answer:
\(3x + 10 = 5x − 30 ⇒ x = 20°\) - Answer:
Draw a parallel line. \(∠XMY = 180° − (120° + 40°) = 20°\) (adjust per Example 4). - Answer:
Angles: \(72°\) and \(108°\) - Answer:
Four right angles around a point sum to \(360°\). - Answer:
\(∠PRD = 127°\) (given). - Answer:
By Theorem 6.6, lines parallel to the same line are parallel to each other. - Answer:
\(∠XMB = 180° − 120° = 60°\) (using interior angles). - Answer:
If bisectors are parallel, original angles are equal ⇒ lines are parallel (Example 5). - Answer:
\(x = 125°\), \(y = 125°\), \(z = 35°\) (similar to Example 6). - Answer:
Using Linear Pair Axiom and Substitution (Theorem 6.1). - Answer:
Angle of incidence = angle of reflection. Parallel mirrors ⇒ \(AB || CD\) (Example 5 logic). - Answer:
Let angles be \(x\). Then \(2x = 180° ⇒ x = 90°\) - Answer:
\(∠PQR = 110°\), \(∠RST = 130°\) (given). \(∠QRS = 60°\) (using auxiliary line). - Answer:
By converse of corresponding angles axiom, lines are parallel. - Answer:
\(∠AGE = 126°\), \(∠GEF = 36°\), \(∠FGE = 54°\) (using perpendicular and angle bisectors).
Related Posts
- Number Systems Class 9 Extra Questions | Mathematics Chapter 1
- Polynomials Class 9 Extra Questions | Mathematics Chapter 2
- Coordinate Geometry Class 9 Extra Questions | Mathematics Chapter 3
The Bottom Line
I hope these extra questions have helped you a lot. Remember, math is all about practice, so don’t hesitate to revisit these questions and explore more on your own. If you found this post Lines and Angles Class 9 Extra Questions helpful, feel free to share it with your friends or classmates who might benefit from it.
If you find any mistake in the above questions and answers or have any other issues regarding the content of this website, feel free to contact us through the Contact Us section.
You can also check the related MCQs for this chapter here: MCQ on Lines and Angles
Thank you for visiting our blog, have a great day.
Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.