Welcome to JNVMaths.com, your trusted source for acing the Jawahar Navodaya Vidyalaya Class 9 Entrance Exam math section. In this comprehensive blog post, we will dissect the essential topic of "Lines and Angles" to equip you with the knowledge and skills needed for success.
Understanding Lines and Angles
Lines and angles form the building blocks of geometry and have immense significance in mathematics. A solid grasp of this topic is crucial for performing well in the entrance exam. We'll break down the key concepts and strategies to help you master "Lines and Angles."
The Basics of Lines
1. Line Segment: A fundamental element in geometry, a line segment is a part of a line with two endpoints.
2. Rays and Lines: Learn the difference between rays (with one endpoint) and lines (infinite in both directions).
3. Intersecting Lines: Explore how lines can intersect at various angles, including acute, obtuse, right, and straight angles.
Understanding Angles
4. What Are Angles?: Gain a comprehensive understanding of what angles are, their measurement, and how to represent them.
5. Types of Angles: Discover different types of angles such as acute, obtuse, right, straight, and reflex angles.
Angle Pairs
6. Complementary and Supplementary Angles: Explore how two angles can be complementary (adding up to 90 degrees) or supplementary (adding up to 180 degrees).
Parallel and Perpendicular Lines
7. Parallel Lines: Learn about lines that run in the same direction and never meet, leading to various properties and theorems.
8. Perpendicular Lines: Understand lines that intersect at right angles and their implications.
Angle Measurement
9. Protractor Use: Get hands-on advice on using a protractor for precise angle measurement.
Applications of Lines and Angles
10. Real-Life Applications: Discover how lines and angles are used in everyday life, from architecture to navigation.
Strategies for Solving Problems
11. Solving Line and Angle Problems: Learn problem-solving techniques, including identifying angles, finding angle measures, and applying theorems.
Diagrams and Visual Aids
12. Visualizing Lines and Angles: To enhance understanding, we'll include diagrams and visual aids that simplify complex concepts.
Practice Questions and Exercises
13. Test Your Knowledge: We'll provide practice questions and exercises to reinforce your understanding.
Stay Connected
14. Subscribe for Updates: Don't miss any valuable content; subscribe for updates on JNVMaths.com.
Join the Community
15. Connect with Us: Follow us on social media to stay connected with the JNVMaths.com community, get additional tips, and stay updated on the latest exam-related news.
प्रश्न:1. जब दो रेखाएं एक-दूसरे को काटती हैं, तो लंबवत विपरीत कोण बनते हैं:
A. असमान
B. बराबर
C. तय नहीं किया जा सकता
D. इनमे से कोई भी नहीं
उत्तर : B. बराबर
प्रश्न:2. जब दो रेखाएं समानांतर होती हैं, तो वे:
A. एक बिंदु पर प्रतिच्छेद करें
B. दो बिंदुओं पर प्रतिच्छेद करें
C. तीन बिंदुओं पर प्रतिच्छेद करें
D. किसी भी बिंदु पर प्रतिच्छेद नहीं करता
उत्तर : D. किसी भी बिंदु पर प्रतिच्छेद नहीं करता
प्रश्न:3. दिए गए चित्र में, यदि ∠GED = 135 ° और AB || CD, EF ⊥ CD, ∠AGE होगी:
A. 120 °
B. 90 °
C. 135 °
D. 140 °
उत्तर : C. 135 °
प्रश्न:4. किसी त्रिभुज में, यदि किसी बाह्य कोण का माप 105° है और उसके सम्मुख आंतरिक कोण बराबर हैं। इन समान कोणों का मान ज्ञात कीजिए
A. 72½°
B. 52½°
C. 75°
D. 37°
उत्तर: B. 52½°
प्रश्न:5. यदि दी गई आकृति में AB, DE के समानांतर है तो x का मान ज्ञात कीजिए
A. 45°
B. 25°
C. 55°
D. 35°
उत्तर : D. 35°
प्रश्न:6. यदि, ∠MXQ = 135° और ∠MYR = 40°. PQ, RS के समानांतर है। ∠XMY ज्ञात कीजिए
A. 90°
B. 60°
C. 85°
D. 55°
उत्तर : C. 85°
प्रश्न:7. यदि कोणों का अनुपात 5:3:7 है। त्रिभुज होगा:
A. एक समद्विबाहु त्रिभुज
B. एक समकोण त्रिभुज
C. एक अधिक कोण वाला त्रिभुज
D. एक न्यूनकोण त्रिभुज
उत्तर : C. एक न्यूनकोण त्रिभुज.
प्रश्न:8. यदि कोणों का अनुपात 2:4:3 है। सबसे छोटे कोण का मान होगा:
A. 40°
B. 80°
C. 60°
D. 20°
उत्तर : A. 40°
प्रश्न:9. दिए गए चित्र से x का मान ज्ञात कीजिए, जहाँ POQ एक रेखा है।
A. 20°
B. 30°
C. 25°
D. 35°
उत्तर : A. 20°
प्रश्न:10. यदि AOB एक रेखा है तो दी गई आकृति में क्रमशः ∠BOC, ∠COD और ∠DOA की माप हैं :
A. 36°, 54°, 90°
B. 90°, 54°, 36°
C. 90°, 36°, 54°
D. 36°, 90°, 54°
उत्तर : A. 36°, 54°, 90°
प्रश्न:11. यदि B, AC पर स्थित है, तो x का मान ज्ञात कीजिए। दिया गया है AB = x + 3, AC = 4x – 5 और BC = 2x.
A. 5
B. 8
C. 3
D. 2
उत्तर : B. 8
प्रश्न:12. एक त्रिभुज के विपरीत आंतरिक कोणों का अनुपात 1:3 है। यह देखते हुए, त्रिभुज का एक बाह्य कोण 80° है। आंतरिक सम्मुख कोणों का मान ज्ञात कीजिए ।
A. 40°, 120°
B. 30°, 60°
C. 20°, 60°
D. 90°, 60°
उत्तर : C. 20°, 60°
Question 1. When two lines intersect each other, perpendicularly opposite angles are formed:
A. unequal
B. equal
C. Cannot be decided
D. None of these
Answer: B. Equal
Question 2. When two lines are parallel, they:
A. intersect at one point
B. intersect at two points
C. intersect at three points
D. Does not intersect at any point
Answer: D. Does not intersect at any point
Question 3. In the given figure, if ∠GED = 135° and AB || CD, EF⊥ CD,∠AGE will be:
A. 120°
B. 90°
C. 135°
D. 140°
Answer: C. 135°
Question:4. In a triangle, if the measure of an exterior angle is 105° and the interior angles opposite to it are equal. Find the value of these equal angles
A. 72½°
B. 52½°
C. 75°
D. 37°
Answer: B. 52½
Question:5. If AB is parallel to DE in the given figure then find the value of x.
A. 45°
B. 25°
C. 55°
D. 35°
Answer: D. 35°
Question:6. If, ∠MXQ = 135° and ∠MYR = 40°. PQ is parallel to RS. Find ∠XMY
A.90°
B.60°
C.85°
D.55°
Answer: C. 85°
Question:7. If the ratio of the angles is 5:3:7. The triangle will be:
A. An isosceles triangle
B. a right triangle
C. An obtuse triangle
D. An acute triangle
Answer: C. An acute triangle.
Question:8. If the ratio of the angles is 2:4:3. The value of the smallest angle will be:
A.40°
B.80°
C.60°
D.20°
Answer: A. 40°
Question:9. Find the value of x from the given figure, where POQ is a line.
A.20°
B.30°
C.25°
D.35°
Answer: A. 20°
Question:10. If AOB is a line then the measures of ∠BOC, ∠COD and ∠DOA respectively in the given figure are :
A. 36°, 54°, 90°
B. 90°, 54°, 36°
C. 90°, 36°, 54°
D. 36°, 90°, 54°
Answer: A. 36°, 54°, 90°
Question:11. If B lies on AC, then find the value of x. Given AB = x + 3, AC = 4x – 5 and BC = 2x.
A.5
B.8
C.3
D.2
Answer: B. 8
Question:12. The ratio of opposite interior angles of a triangle is 1:3. Given that, one exterior angle of the triangle is 80°. Find the value of interior opposite angles.
A. 40°, 120°
B. 30°, 60°
C. 20°, 60°
D. 90°, 60°
Answer: C. 20°, 60°
Conclusion:
With this comprehensive guide on "Lines and Angles," you're well on your way to mastering this fundamental geometry topic and excelling in the JNV Class 9 Entrance Exam. Remember, practice makes perfect. Keep revising, solving problems, and staying updated with the latest exam-related information. Your journey to success starts with a strong foundation in math, and we're here to support you every step of the way. Good luck, and stay tuned to JNVMaths.com for more math excellence!
Comments